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Atoms and Nuclei Part 1

Section: Physics

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Question : 2 of 100

Marks: +1, -0

According to Bohr atom model, in which of the following transitions will the frequency be maximum ?

[24 Feb 2021 Shift 2]

$n=4$ to $n=3$
$n=2$ to $n=1$
$n=5$ to $n=4$
$n=3$ to $n=2$

Solution:

Let

n_f, n_i

be the final and initial orbit.

As we know that,

\,\frac{1}{\lambda}=109\times10^{7}\left[\,\frac{1}{n_{f}^{2}}-\,\frac{1}{n_{i}^{2}}\right]

Now, checking for each option, we get

(a)

\,\frac{1}{\lambda}\propto\left[\,\frac{1}{3^{2}}-\,\frac{1}{4^{2}}\right]=\left[\,\frac{1}{9}-\,\frac{1}{16}\right]=0.05

\dots

(i)

(b)

\,\frac{1}{\lambda}\propto\left[\,\frac{1}{1}-\,\frac{1}{4}\right]=0.75

... (ii)

(c)

\,\frac{1}{\lambda}\propto\left[\,\frac{1}{16}-\,\frac{1}{25}\right]=0.0225

... (iii)

(d)

\,\frac{1}{\lambda}\propto\left[\,\frac{1}{4}-\,\frac{1}{9}\right]=0.14

... (iv)

The option (b) has highest value.

Since, frequency,

f = \,\frac{C}{\lambda} \Rightarrow f \propto \,\frac{1}{\lambda}

\therefore

Frequency will be maximum for transition

n=2

to

n=1

.

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