Question

In which of the following transitions will the wavelength be minimum? 

पर्याय

•  n = 5 to n = 4

•  n = 4 to n = 3

• n = 3 to n = 2

• n = 2 to n = 1

Answer 1

 n = 2 to n = 1

For the transition in the hydrogen-like atom, the wavelength of the emitted radiation is calculated by

`1/lamda = RZ^2 (1/n^1 - 1/n^2)`

Here, R is the Rydberg constant.

For the transition from n = 5 to n = 4, the wavelength is given by

`1/lamda = RZ^2 (1/4^2 - 1/5^2)`

`lamda = 400/(9RZ^2)`

For the transition from n = 4 to n = 3, the wavelength is given by

`1/lamda = RZ^2 (1/3^2 - 1/4^2)`

`lamda = (144)/ (7RZ^2)`

For the transition from n = 3 to n = 2, the wavelength is given by

`1/lamda = RZ^2 (1/2^2 - 1/3^2 )`

`lamda = (36)/(5RZ^2)`

For the transition from n = 2 to n = 1, the wavelength is given by

`1/lamda = RZ^2 (1/2^2 - 1/3^2)`

`lamda = 2/(RZ^2)`

From the above calculations, it can be observed that the wavelength of the radiation emitted for the transition from n = 2 to n = 1 will be minimum.