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Question: The frequency of light emitted for the transition n = 4 to n = 2 of He+ is equal to the transition i...

The frequency of light emitted for the transition n = 4 to n = 2 of He+ is equal to the transition in H atom corresponding to which of the following?

A

n = 2 to n = 1

B

n = 3 to n = 2

C

n = 4 to n = 3

D

n = 3 to n = 1

Answer

n = 2 to n = 1

Explanation

Solution

hn = DE = 13.6 z2 (1n121n22)\left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right)

υ He+ = υH × z2 \upsilon_{\text{ He+}}\text{ = }\upsilon\text{H }\text{×}\text{ }\text{z}^{2}\

(1(n12)21(n22)2)\left( \frac{1}{\left( \frac{n_{1}}{2} \right)^{2}} - \frac{1}{\left( \frac{n_{2}}{2} \right)^{2}} \right)

=υH(1(22)21(42)2)= \upsilon H\left( \frac{1}{\left( \frac{2}{2} \right)^{2}} - \frac{1}{\left( \frac{4}{2} \right)^{2}} \right)

For H-atom

n1 = 1, n2 = 2