Question

An electron in H-atom jumps from nth orbit to 3rd
orbit. If three spectral lines are possible for the
transition, the value of n is
(1) 4
(2) 5
(3) 7
(4) 6
​

Answer 1

The correct option about the value of n is (2) 5.

Given:

An electron in H-atom jumps from the nth orbit to the 3rd orbit and three spectral lines are possible for transition.

To Find:

The value of n.

Solution:

To find the value of n we will follow the following steps:

The number of spectral lines can be calculated by the formula =

$\frac{(n2 - n1)(n2 - n1 + 1)}{2}$

Here, n2 is the orbit after the jumping of an electron from the n1 orbit.

When an electron jump from a higher level to a lower level then energy is released while jumping off an electron from a lower to higher energy involves the absorption of energy.

As given in the question number of spectral lines produced is 3.

n2 = n and n1 = 3

So,

Putting values of n2 and n1 we get,

$\frac{(n - 3)(n - 3 + 1)}{2} = 3$

$\frac{(n - 3)(n - 2)}{2} = 3$

${n}^{2} - 5n \: + 6 = 6$

${n}^{2} = 5n$

n = 5

Henceforth, the value of n is 5.

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