Question

question 2

Physical constants: • Planck constant h = 6.626 X 10 -34 J.S • Speed of light c = 2.998 x 108 m/s Please use the correct significant figures and units for your final answer. Question 1 What is the time-independent Schrödinger equation and what is the time-dependent Schrödinger equation for a 1-dimensional system (x)? Explain each term in them. What do we usually know and what do we usually try to solve? Question 2 Calculate the wavelength and the frequency of the photon emitted from transition n = 3 to n=1 in hydrogen atom using Bohr's model. What type of radiation does this belong to (in the frequency range of electromagnetic spectrum)?

Answer 1

Solution:

According to equation of wavelength and Rydberg constant (RH),

1/$\lambda$ = RH [1/n2^2 - 1/n1^2]

Where,

RH = 1.097 x 10^7  m-1

n1 = 3

n2 = 1

Therefore,

1/$\lambda$ = 1.097 x 10^7 m-1 [ 1/(1)^2 - 1/(3)^2]

= 1.097 x 10^7 x (1/1 - 1/9) m-1

= 1.097 x 10^7 x ( 8/9) m-1

= (8.776 x 10^7 / 9) m-1

= 0.97511 x 10^7 m-1

$\lambda$ = 1 / ( 0.97511 x 10^7) m

= 1.02553 x 10^-7 m

= 102.553 x 10^-9 m

$\lambda$ = 102.55 nm

Frequency (v) is calculated as,

v = c/$\lambda$ = 2.998 x 10^8 m s-1 / 1.0255 x 10^-7 m

= 2.9234 x 10^15 s-1

= 2.923 x 10^15 s-1

The value of wavelength 102.55 nm and frequency 2.923 x 10^15 s-1 belongs to UV region.

Hence, transition occurs in UV region.