Question

What is the wavelength of light emitted when the electron in a

hydrogen atom undergoes transition from an energy level with n = 3 to n = 1?​

Answer 1

Answer:-

The wavelength of light emitted is 102 nm .  

Explanation:-  

According to Rydberg's formula :-

ṽ(cm⁻¹) = 109677[1/n²₁ - 1/n²₂]  

In the present case :-

• n₂ = 3

• n₁ = 1  

⇒ ṽ = 109677[1/(1)² - 1/(3)²]

⇒ ṽ = 109677[1/1 - 1/9]

⇒ ṽ = 109677[8/9]

⇒ ṽ = 97491 cm⁻¹  

Now :-  

λ = 1/ṽ  

⇒ λ = 1/97491 cm

⇒ λ = 1.02×10⁻⁵ cm

⇒ λ = 1.02×10⁻⁵×10⁷ nm

⇒ λ = 102 nm

Answer 2

Required Answer :-

ṽ (cm-1) = 109677[1/n²₁ - 1/n²₂]

ṽ = 109677[1/1² - 1/3²]

ṽ  = 109677[1/1 - 1/9]

ṽ  = 109677[9 - 1/9]

ṽ  = 97491 cm-1

Now

$\sf \lambda = 1/v$

λ = 1/97491

λ  = 1.02 × 10-5 × 10-7

• According to exponential law

λ= 102 nm