This document contains 3 multiple choice questions related to Bohr's model of the hydrogen atom and diffraction gratings. Question 1 asks to calculate the angle of the 4th interference maximum for light of wavelength 670 nm incident on a diffraction grating with 0.1 mm slits. Question 2 asks which equation describes the visible emission spectrum of the hydrogen atom according to Bohr's model. Question 3 has two parts: a) asking for the largest wavelength emitted by the Balmer series, and b) calculating the corresponding frequency using the wavelength from part a).

1. 1. A plane laser light of wavelength 670 nm is incident normally on a plane diffraction grating
with slit width of 0.1 mm what is the angle of the m=4 interference maximum?
A) 1.54 o
B) 0.3 o
C) 35 o
D) 90 o
2. According to Bohr’s model, which of the following describes the visible emission spectrum of
the hydrogen atom?
A) = R() B) = R() C) = R()
D) = R()
3. Based on Bohr’s model for the hydrogen atom,
a) What is the largest wavelength emitted from the Balmer series?
i) ~410 nm ii) ~550 nm iii) ~660 nm iv) ~700 nm
b) What is the corresponding frequency? (Use the answer for the wavelength from (a))
i) 460 x 10 12
Hz ii) 480 x 10 12
Hz iii) 454 x 10 12
Hz iv) 512 Hz
Solution
1)
here,
wavelength , lamda = 670 nm = 6.7 * 10^-7 m
slit width, d = 0.1 mm = 1 * 10^-4 m
m = 4
let the angle of the interference maximum be theta

2. d * sin(theta) = m * lamda
1* 10^-4 * sin(theta) = 4 * 6.7 * 10^-7
solving for theta
theta = 1.54 degree
the angle is A) 1.54 degree