Advertisement Remove all ads

In Which of the Following Transitions Will the Wavelength Be Minimum? - Physics

MCQ

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

Options

  •  n = 5 to n = 4

  •  n = 4 to n = 3

  • n = 3 to n = 2

  • n = 2 to n = 1

Advertisement Remove all ads

Solution

 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.

Concept: The Line Spectra of the Hydrogen Atom
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 21 Bohr’s Model and Physics of Atom
MCQ | Q 4 | Page 383
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×