Topic: Quantum Theory
Problem-1: Sketch the plots of “Intensity of radiation” vs “wavelength” for Black-body
radiation experiment performed at 1000 K and 1500 K. Also, sketch Rayleigh –Jeans (R-J) law
based plot. What was the drawback of R-J law? (Sketch all plots under the same axes).
Drawbacks:
1. R-J law cannot explain the curve at lower wavelengths
2. Even cold objects would emit UV rays
Problem-2: A sodium light emits yellow light (500 nm). How many photons it emits each
second if its power is 100 W?
Ans. Energy emitted per second = 100 J
Energy of each photon = h = hc/ = 6.626 x 10-34 Js x 3 x 108 ms-1/500 x 10-9 m
= 3.98 x 10-19 J
Number of photons emitted per second = 100 J / 3.98 x 10-19 J = 2.5 x 1020
Problem-3: The maximum emission of the Sun occurs at λmax = 490 nm. What is it’s surface
temperature?
λmax.T = constant which is equal to 2.99 x 10-3 m.K
490 x 10-9 m x T = 2.99 x 10-3 m K
T = 6102 K
Problem-4: A glow worm emits red light of λ = 650 nm. If this light was a radiation from hot
source, what would be the temperature? What do you conclude from your value?
λmax.T = constant which is equal to 2.99 x 10-3 m.K
650 x 10-9 m x T = 2.99 x 10-3 m K
T = 4600 K
This is a photophysical/photochemical process and not a light emitted by a hot body. This
formula is not applicable in this case.
Problem-5: Calculate the power radiated by a blackbody at temperature 3000 K if this
blackbody known to radiate 0.4 W at 1500 K.
Emittance (M) = Power/area of the emitter = a.T4
Or, P / Area = a.T4
M = a.T4 where a = 5.67 × 10−8 W.m-2.K-4
P1500K = 0.4 W = Area x a x (1500 K)4
P3000 K = Area x a x (3000 K)4
P3000 K / P1500K = P3000 K /0.4 W = (3000)4/(1500)4
Therefore, P3000 K = 0.4 W x 24 = 6.4 W