# 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

#### 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
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#### 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