Question

Calculate the wavelength and frequency emitted for an electron in H atom from 6th level to the ground state ( n= 1 ). In which region the spectral line belongs to?

Answer 1

Here we can consider Rydberg's equation,
i.e ,
     1/λ = R [ 1/n₁² - 1/n₂² ]

Here, 
        1/λ   is the wave number
        R is the Rydberg's constant ( 109677 )
        n₁ , n₂ represents the region in spectral line. ( n₁ = 1 & n₂  = 6)

Using Rydberg's equation,
      
     1/λ   = 109677 [ 1/1² - 1/6² ]
             =109677 × 0.9722
             = 106630.9777 cm⁻¹ //
    ∴ λ    = 1/106630.977
             = 9.37 × 10⁻⁶ cm //
F ( frequency) = C / λ
              = 3 × 10¹⁰ / 9.37 × 10⁻⁶  [ used 3 × 10¹⁰ coz answer should be in centimeters ]
               = 3.19 × 10¹⁵
               = 3.2 ×10¹⁵ Hz //

∴ λ = 9.37 × 10⁻⁶ cm  
             &
   F = 3.2 ×10¹⁵ Hz

Since, n₁ = 1 , the radiation belongs to UV REGION