Numericals on Wave number and Radius

 

Q1. Calculate the wave number and wavelength of Balmer series of hydrogen spectrum in which electron jumps from orbit 3 to orbit 2.

Solution

Calculation of Wave Number

Here;

R_H = 1.0968553 x 10⁷ m^-1

n₁ = 2

n₂ = 3

Z  = 1

Calculation of Wave Length 

Q2. What is the wavelength and wave number of radiation that is emitted when a hydrogen atom undergoes a transition from orbit 3 to orbit 1.

Solution

Calculation of Wave Number 

R_H = 1.0968553 x 10⁷ m^-1

n₁ = 1

n₂ = 3

Q3.   Calculate the ratio of radius of second and third orbit of hydrogen atom. (Bohr’s radius =  0.529ºA)

Solution 

Q4. If the radius of first Bohr orbit is ‘x’ then calculate 

the radius of the third orbit of hydrogen. 

Solution 

Q1.Calculate the energy of the electron in the                        ground state and first excited state of the                      hydrogen atom

Solution

Part (A)

Z for H = 1

n for ground state = 1