Question

Energy levels A, B, C of acertain atom corresponding to increasing value of energy, i.e., E_A< E₈ < E_e. If λ₁, λ₂ and λ₃ are the wavelength of radiations corresponding to the transitions C to B, B to A and C to A respectively, which of the following statements is correct?

Options

• λ₃ = λ₁ + λ₂

• λ₁ = `(lambda_1lambda_2)/(lambda_1 + lambda_2)`

• λ₁ + λ₂ + λ₃ = 0

• `lambda_3 ^2 = lambda_1 ^2 + lambda_2^2`

Answer 1

λ₁ = `(lambda_1lambda_2)/(lambda_1 + lambda_2)`

Explanation:

(E_C - E_B) + (E_B - E_A) = E_C - E_A 

`Delta "E"_"CB" + Delta "E"_"BA" = Delta "E"_"CA"`

As we know,

`Delta "E"_"a" = "hc"/lambda_"n"` then,

`"hc"/lambda_1 + "hc"/lambda_2 = "hc"/lambda_3`

`1/lambda_1 + 1/lambda_2 = 1/lambda_3`

`=> lambda_3 = (lambda_1 lambda_2)/(lambda_1 + lambda_2)`