DETERMINATION OF β SPECTROSCOPY OF 22Na AND 90Sr IN BOTH THE POSITIVE AND NEGATIVE DIRECTION OF THE MAGNETIC FIELD USING THE SPECTROMETER.

1. KWAMENKRUMAH UNIVERSITYOF SCIENCEAND TECHNOLOGY
COLLEGEOF SCIENCE
DEPARTMENT OF PHYSICS
EXPERIMENT TITLE
DETERMINATION OF βSPECTROSCOPY OF 22
Na AND 90
Sr IN BOTH THE
POSITIVE AND NEGATIVEDIRECTION OF THE MAGNETIC FIELD USING THE
SPECTROMETER.
NAMES INDEX NUMBER
NDEDE ANTHONY 1049013
DOUGLAS OFOSU NKETIA 1049413
GROUP ONE Date:29th
October, 2014.

2. ABSTRACT
An experiment was performed on the study of the β spectroscopy of 90Srand 22Na
in both positive and negative directions of the magnetic field produced by the
current passing through the spectrometer. The iron component was firmly fixed in
position to ensure satisfactory and constant harmonization of magnetic forces. The
zero point was adjusted on the Teslameter before the tangential hallprobe is
introduced through the lateral opening of the spectrometer. The relationship
between the coil current and magnetic flux density was determined. The β-instable
nuclei emit electrons or positrons with a continuous momentum and energy
distribution, because this decay involves three partners in the outgoing channel: an
e±, a neutrino and the final nucleus. Measurements were carried out in both
directions of the magnetic field. The source and the counter tube were inserted, the
Geiger-Muller counter connected and, after establishing the correct direction of the
magnetic field, the counting rate per 10 s measurement period was determined at
different field strengths. The measurement was recorded for both elements,
determining in each case the zero effect with the source but in opposite directions
of the field. A graph of the Number of counts was plotted against the selected
kinetic energies of the particles. From the calculations and graph drawn, the decay
energy of the sodium isotope (22 Na) and strontium isotope (90 Sr) was found out to
be 900±0.05×103J and 2490±0.05×103J respectively. These two values ±0.05and
±0.05 accounted for the errors associated with the two elements during the
performance of the experiment. The errors are therefore due to systematic
measurement errors.

3. EXPERIMENTAL SETUP
Set-up for experimental determination of beta spectroscopy of 22
Na and 90
Sr
APPARATUS NEEDED
1. Teslameter
2. Radioactive Source
3. Tangential Hallprobe
4. Coil
5. Digital Multimeter
6. Power Supply
Teslameter
Geiger-Muller
counter
Power supply
Digital multimeter
Tangential hallprobe
Radioactive source
Coil

4. 7. Geiger Muller Counter
OBSERVATION TABLE:
Measurements of β-spectra of 22
Na in the positive direction in the magnetic
field. TABLE ONE
Current Reading
(I/A)
Geiger-Müller
Counter
Teslameter
Reading/mT
𝑬 𝒌𝒊𝒏/𝟏𝟎−𝟏𝟎
J
0.08 6 13.1 0.314
0.16 11 20.3 0.487
0.24 9 27.3 0.655
0.32 7 35.6 0.855
0.40 7 42.7 1.025
0.48 4 50.0 1.201
0.56 9 57.2 1.374
0.64 6 64.8 1.556
0.72 4 71.8 1.725
0.80 9 80.0 1.922
0.88 6 90.0 2.162
0.96 3 96.0 2.306
1.04 5 102.4 2.460
1.12 7 110.8 2.662
1.20 6 118.5 2.847
1.28 4 124.4 2.989
1.36 11 131.8 3.166
1.44 8 139.6 3.354
1.52 7 146.2 3.512

5. 1.60 9 154.3 3.707
Measurements of β-spectra of 22
Na in the negative direction in the magnetic
field. TABLE TWO
Current Reading
(I/A)
Geiger-Müller
Counter
Teslameter
Reading/mT
𝑬 𝒌𝒊𝒏/𝟏𝟎−𝟏𝟎
J
- 0.08 27 -12.1 0.290
- 0.16 41 -18.7 0.449
- 0.24 45 -25.3 0.607
- 0.32 43 -32.5 0.780
- 0.40 49 -41.8 0.980
- 0.48 32 -48.4 1.162
- 0.56 29 -55.3 1.328
- 0.64 25 -63.5 1.525
- 0.72 18 -70.0 1.691
- 0.80 11 -78.7 1.890
- 0.88 9 -85.8 2.061
- 0.96 14 -94.4 2.268
- 1.04 11 -100.7 2.419
- 1.12 7 -109.0 2.618
- 1.20 23 -114.0 2.739
- 1.28 19 -121.5 2.919
- 1.36 20 -128.1 3.077
- 1.44 25 -134.4 3.229
- 1.52 27 -142.2 3.416
- 1.60 20 -148.2 3.560

6. Measurements of β-spectra of 90
Sr in the positive direction in the magnetic
field. TABLE THREE
Current Reading
(I/A)
Geiger-Müller
Counter
Teslameter
Reading/mT
𝑬 𝒌𝒊𝒏/𝟏𝟎−𝟏𝟎
J
0.08 27 12.7 0.304
0.16 38 19.0 0.456
0.24 66 26.0 0.624
0.32 97 32.9 0.790
0.40 120 40.6 0.975
0.48 141 47.9 1.150
0.56 172 55.8 1.340
0.64 181 63.8 1.532
0.72 220 70.5 1.693
0.80 218 78.1 1.876
0.88 221 85.4 2.051
0.96 215 93.0 2.234
1.04 201 101.0 2.426
1.12 187 107.9 2.592
1.20 157 115.8 2.782
1.28 155 122.7 2.948
1.36 138 129.4 3.109
1.44 108 136.8 3.286
1.52 104 143.3 3.443
1.60 74 149.8 3.599

7. Measurements of β-spectra of 90
Sr in the negative direction in the magnetic
field. TABLE FOUR
Current Reading
(I/A)
Geiger-Müller
Counter
Teslameter
Reading/mT
𝑬 𝒌𝒊𝒏/𝟏𝟎−𝟏𝟎
J
- 0.08 18 -13.7 0.328
- 0.16 13 -19.3 0.463
- 0.24 11 -25.8 0.619
- 0.32 16 -33.2 0.797
- 0.40 4 -40.3 0.968
- 0.48 4 -46.8 1.124
- 0.56 3 -54.5 1.309
- 0.64 3 -61.6 1.479
- 0.72 4 -70.2 1.686
- 0.80 5 -77.1 1.852
- 0.88 5 -84.3 2.025
- 0.96 5 -91.9 2.208
- 1.04 6 -99.6 2.393
- 1.12 6 -106.2 2.551
- 1.20 5 -114.1 2.741
- 1.28 5 -120.3 2.890
- 1.36 5 -126.9 3.049
- 1.44 2 -133.7 3.212
- 1.52 6 -140.7 3.380
- 1.60 2 -146.8 3.527

8. THE GRAPHS OF CORRESPONDING TABLEVALUES
GRAPH ONE: β Spectrumof 22
Nain the positive directionof the magnetic field.
0
2
4
6
8
10
12
0 0.5 1 1.5 2 2.5 3 3.5 4
NumberofCounts(N)
EKin/J
A GRAPH OF NUMBER OF COUNTS(N) AGAINSTE

9. GRAPH TWO: β Spectraof 22
Na in the negative directionof the magnetic field.
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3 3.5 4
NumberOfCounts(N)
Ekin
A GRAPH OF NUMBER OF COUNTS(N) AGAINSTEkin/J

10. GRAPH 3: β Spectraof 90
Sr inthe positive directionof the magnetic field.
0
0.5
1
1.5
2
2.5
3
3.5
4
0 50 100 150 200 250
NumberofCounts(N)
Ekin /J
A GRAPH OF NUMBER OF COUNTS(N) AGAINST

11. GRAPH 4: β Spectraof 90
Sr inthe negative directionof the magnetic field.
0
2
4
6
8
10
12
14
16
18
20
0 0.5 1 1.5 2 2.5 3 3.5 4
NumberofCount(N)
Ekin/J
A GRAPH OF NUMBER OF COUNT(N) AGAINST

12. THEORY
β- Particles are selected in the β-spectroscope on the basis of their energy by obliging
them to follow a fixed orbit using diaphragm in a homogeneous magnetic field. In this
orbit the Lorentz force, due to the magnetic cross-field, and the centrifugal force are in
equilibrium: e v m =
𝑚𝑣2
𝑟
. This yields the following expression for the momentum, p = m
v = e B r. The equation for relativistic particles with the momentum is: 𝐸 𝑇
2
=𝑝2
𝑐2
+
𝑚0 𝑐4
. Then,
𝐸2
𝑐2 = 𝑝2
+ 𝑚 𝑜
2
𝑐2
, where E denote the total energy of the particles, made up
of kinetic energy, 𝐸 𝑘𝑖𝑛 and the resting energy, 𝑚0 𝑐2
.
Also E = 𝐸 𝑘𝑖𝑛 + 𝑚0 𝑐2
. The Kinetic Energy is accordingly given as: 𝐸 𝑘𝑖𝑛 =
√(𝑒𝐵𝑟𝑐)2 + 𝑚0
2
−𝑚0 𝑐2
.
With a given orbital radius of r = 50 mm, it is possible to fix a specific particle energy for
each magnetic field strength and for each current strength .The process of 𝛽–decay in the
atomic nucleus results in the conversation of a neutron n into a proton p and an electron e,
which leaves the nucleus, and into an antineutrino (v) which is difficult to detect.
𝛽+
-decay causes the occurrence of a positron, in which case the decay equation will be
given as: p = n + 𝑒−
+ 𝑣. The decay energy, 𝐸 𝑧 is released during the conversion. Since
the neutrino carries with it a proportion of the decay energy, the magnitude of which
cannot be determined, a continuous energy distribution occurs in which all the energy
values from 0 to 𝐸 𝑧 occur. A further characteristic of the beta-spectrum is its most
frequent energy Eh which will always be one third of the maximum energy E2: Eh =
1
3
Ez.
The most frequent energy Eh can be determined with a very much greater accuracy than
the maximum energy Ez, since at the upper end, the spectrum passes with a flat slope into
the zero effect.

13. CALCULATION
Using the formula:
𝐸 𝐾𝑖𝑛𝑒𝑡𝑖𝑐 = √(𝑒𝐵𝑟𝑐)2 + (𝑚 𝑜)2 𝐶2 − 𝑚 𝑜 ∙ 𝑐2
Where the technical specifications and physical constants are
Average trajectory radius, r = 50 mm = 0.05 m
Speed of the particle (element) 𝑐 = 3.0 × 108
𝑚/𝑠
Mass of particle (element) 𝑚 𝑜 = 9.102 × 10−31
𝐾𝑔
Charge of the particle (element) 𝑒 = 1.602 × 10−19
𝐶
Magnetic field flux, B
𝐸 𝐾𝑖𝑛 = √{(1.602 × 10−19)(0.05)(3.0 × 108)( 𝐵)}2 + (𝑚 𝑜)2 𝐶4 − 𝑚 𝑜 ∙ 𝑐2
𝐸 𝐾𝑖𝑛 = √{(2.403 × 10−12)( 𝐵)}2 + {(9.10 × 10−31)2(3.0 × 108)4} − 𝑚 𝑜 ∙ 𝑐2
𝐸 𝐾𝑖𝑛 = √{(2.403 × 10−12)( 𝐵)}2 + 6.71 × 10−27 − {(9.10 × 10−31
) ∙ (2.998 × 108)2
}
𝐸 𝐾𝑖𝑛 = √{(2.403 × 10−12)( 𝐵)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
For The Measurementwith a Source in the Positive Directionof Current
Using Sodium (22
Na)
a) When magnetic flux, B = 13.1mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(13.1)}2 + 6.71 × 10−27 − (8.19 × 10−14
)

14. 𝐸 𝐾𝑖𝑛 = 0.314 × 10−10
𝐽
b) When magnetic flux, B = 20.3 mT
𝐸 𝐾𝑖𝑛 = √{(2.403 × 10−12)(20.3)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.487× 10−10
𝐽
c) When magnetic flux, B = 27.3mT
𝐸 𝐾𝑖𝑛 = √{(2.403 × 10−12)(27.3)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.655× 10−10
𝐽
d) When magnetic flux, B = 35.6mT
𝐸 𝐾𝑖𝑛 = √{(2.403 × 10−12)(35.6)}2 + 6.693 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.855× 10−10
𝐽
e) When magnetic flux, B 42.7mT
𝐸 𝐾𝑖𝑛 = √{(2.403 × 10−12)(42.7)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 1.025× 10−10
𝐽
f) When magnetic flux, B = 50.0mT
𝐸 𝐾𝑖𝑛 = √{(2.403 × 10−12)(50.0)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 1.0201 × 10−10
𝐽

15. For The Measurementwith a Source in the negative Directionof Current
Using Sodium (22
Na)
a) When magnetic flux, B = -12.1 mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(−12.1)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.290× 10−10
𝐽
b) When magnetic flux, B = -18.7 mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(−18.7)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.449× 10−10
𝐽
c) When magnetic flux, B = -25.3mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(−25.3)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.607× 10−10
𝐽
d) When magnetic flux, B = -32.5mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(−32.5)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.780× 10−10
𝐽

16. e) When magnetic flux, B = -41.8mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(−41.8)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.980× 10−10
𝐽
f) When magnetic flux, B =-55.3 mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(−55.3)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 1.328× 10−10
𝐽
g) When magnetic flux, B =-63.5 mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(−63.5)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 1.525× 10−10
The rest of the energies were calculated from the same format
For The Measurementwith a Source in the positive Direction of Current
Using Strontium (90
Sr)
a) When magnetic flux, B = 12.7 mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(12.7)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.304× 10−10
𝐽
b) When magnetic flux, B = 19.0mT

17. 𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(19.0)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.456× 10−10
𝐽
c) When magnetic flux, B = 26.0mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(26.0)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.624× 10−10
𝐽
d) When magnetic flux, B = 32.9mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(32.9)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.790× 10−10
𝐽
e) When magnetic flux, B = 40.6mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(40.6)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.975× 10−10
𝐽
f) When magnetic flux, B = 47.9 mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(47.9)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 1.150× 10−10
The rest of the energies were calculated from the same format

18. For The Measurementwith a Source in the negative Directionof Current
Using Strontium (90
Sr)
a) When magnetic flux, B = -13.7mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(−13.7)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.328× 10−10
𝐽
b) When magnetic flux, B =-19.3mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(−19.3)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.463× 10−10
𝐽
c) When magnetic flux, B = -25.8mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(−25.8)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.619× 10−10
𝐽
d) When magnetic flux, B = -33.2mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(−33.2)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 0.797× 10−10
𝐽
e) When magnetic flux, B = -46.8mT
𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(−46.8)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 1.124× 10−10
𝐽
f) When magnetic flux, B = -54.5mT

19. 𝐸 𝐾𝑖𝑛 = √{(2.4014 × 10−12)(−54.5)}2 + 6.71 × 10−27 − (8.19 × 10−14
)
𝐸 𝐾𝑖𝑛 = 1.309× 10−10
The rest of the energies were calculated from the same format.
CALCULATION OF BETA DECAY
For decay energy, Ez of 22 Na;
The genera l formula is given as
Eh= Ez/3……………..where Ez is the decay energy, Eh is the maximum energy
EZ = 3(210+ 30×103ev) =900×103J
Also; for Decay Energy, EZ of 90 Sr;
Eh = (740+30 KeV)
EZ = 3(740+30 KeV) =2490×103J

20. ERROR ANALYSIS
Using the formula, standard deviation, Σ = √
(𝑥−𝔵)2
𝑛(𝑛−1)
…………………eqn.(1)
and σ =
Σ
√𝑛
…………………………eqn. (2)
Where σ represents standard deviation error
x represents values for energies
𝖝 represents the mean value for x
n represents the total number of elements in the x values.
The error obtained were systematic errors which were associated with the energies
due to difference in the magnetic flux of the two different elements.
For Sodium Isotope;
Y = 0.314+0.487+0.655+0.855+1.025+1.201+1.374+1.556+1.725+1.922+2.162+
2.306+2.460+2.662+2.847+2.989+3.166+3.354+3.152+3.707 = 39.28
Hence Mean(x) =
𝑌
20
=
39.28
20
= 1.964

21. X x- 𝖝 (x-𝖝)2
0.314 1.650 2.723
0.487 1.477 2.181
0.650 1.314 1.727
0.855 1.109 1.230
1.025 0.939 0.882
1.201 0.763 0.582
1.374 0.590 0.348
1.556 0.408 0.166
1.725 0.239 0.057
1.922 -0.028 0.0008
2.162 -0.198 0.039
2.306 -0.342 0.117
2.460 -0.496 0.246
2.662 -0.698 0.487
2.847 -0.883 0.780
2.989 -1.025 1.051
3.160 -1.196 1.430
3.354 -1.390 1.932
3.512 -1.548 2.400
3.707 -1.743 3.038

22. Total (x-𝖝)2=19.700
Therefore standard deviation Σ = √
19.700
20(20−1)
=0.2277=0.228
Hence the error, σ =
0.228
√𝑛
=
0.282
√20
= ±0.05098 ≅ ±0.05
For Strotium Isotope;
Z = 0.304+0.456+0.624+0.79+0.975+1.15+1.34+1.532+1.693+1.876+2.051+2.234
+2.426+2.592+2.946+3.109+3.286+2.443+3.599 = 39.21
Mean(x) =
𝑍
20
=
39.21
20
= 1.961

23. X x- 𝖝 (x-𝖝)2
0.304 -1.656 2.742
0.456 -1.504 2.262
0.624 -1.336 1.785
0.790 -1.170 1.369
0.975 -0.985 0.970
1.150 -0.810 0.656
1.340 -0.620 0.384
1.532 -0.428 0.183
1.693 0.267 0.071
1.876 0.084 0.007
2.051 0.091 0.008
2.234 0.274 0.075
2.426 0.466 0.217
2.592 0.632 0.400
2.782 0.822 0.676
2.948 0.988 0.976
3.109 1.149 1.320
3.286 1.326 1.758
3.443 1.483 2.199
3.599 1.639 2.686

24. Total(x-𝖝)2 = 21.744
Therefore standard deviation, Σ = √
21.742
20(`20−1)
= √
21.744
20(`19)
= 0.23920 = 0.239
Hence the error σ,=
0.3112
√𝑛
=
0.239
20
=±0.0534 ≅ ±0.05

25. RESULTS AND DISCUSSIONS
From the graphs, it was analyzed that the field direction of the magnetic field varied in
some of the experiments due to the changes in the direction of the current. When the
graphs were plotted, it was seen that, there was a beta decay which rose to a peak and
returned downward but could not reach the zero mark. This is the sodium (22Na) beta
decay. The gently intensified background in the 22Na spectrum was attributed to the
ability to emit low radiations (energy) hence, has lower energy decay. The probability of
the response of the counter tube and the resolution of the spectrometer were energy-
dependent. On the other hand, there was beta decay which rose to a peak and continued
upward. This is the strontium (90Sr) beta decay. This also which is in the(90Sr) spectrum
was attributed to the ability to emit high radiations (energy) hence, has the greatest
energy decay However, the spectra were as a result distorted, although this did not affect
their predictive value in relation to their energies. Several fractions of the spectra were
available in both cases. From the calculations and graph drawn, the decay energy of the
sodium isotope (22 Na) was found out to be 900± 0.05×103J and that of strontium isotope
(90 Sr) to be 2490±0.05×103J .It was observed from the table of results that as the current
increased, the magnetic field also increased resulting in increasing energy. It was also
observed that the isotopes produced lower values of counts for the negative magnetic
fields for strontium isotope and vice versa for sodium isotope. From the graphs, it was
noticed that the spectra were made up of many fractions in both cases. The irregularities
in the spectral lines were due to the fact that the interval width per energy measurement is
a momentum window and not an energy window. Also the probability of response of the
counter tube and the resolution of the spectrometer are energy dependent. As a result of
the above reasons the spectra are therefore distorted although this does not affect their
predictive values in relation to the energies. The errors are therefore due to systematic
measurement errors.

26. PRECAUTIONS
It was ensured that;
1. The instruments were used in dry rooms in which there is no risk of explosion.
2. The connections for the set-up were very tight.
3. The main supply voltage corresponds to that given on the type plate fixed to the
instrument.
CONCLUSION
The β- spectra of 90Sr and 22Na in the two different types of beta decay; positive
and negative directions were determined in this experiment. The probability of
response of the counter tube and the resolution of the spectrometer are energy-
dependent. From the calculations and graph drawn, the decay energy of the sodium
isotope (22 Na) and strontium isotope (90 Sr) was found out to be 900±0.05×103J
and 2490±0.05×103J respectively. From these results obtained, it was also deduced
that the decay energy of the sodium isotope was much smaller than the strontium
isotope. It was not obvious how a nucleus can emit an electron if there aren’t any
electrons in the nucleus but at the end the experiment our aim for the experiment
which was determining the spectrum, the decay energy of 90Srand 22Na was met.