Question

if wave number of radiation is 20 m-1 then frequency of the radiation will be

Answer 1

Answer : The frequency of the radiation will be, $6\times 10^9s^{-1}$

Solution : Given,

Wave number of radiation = $20m^{-1}$

First we have to calculate the wavelength of radiation.

Formula used : $\lambda=\frac{1}{\bar{\nu }}$

where,

$\lambda$ = wavelength of radiation

$\bar{\nu }$ = wave number of radiation

Now put all the given values in this formula, we get

$\lambda=\frac{1}{20m^{-1}}=0.05m$

Now we have to calculate the frequency of radiation.

Formula used : $\nu=\frac{c}{\lambda}$

where,

$\nu$ = frequency of radiation

$\lambda$ = wavelength of radiation

c = speed of light = $3\times 10^8m/s$

Now put all the given values in this formula, we get

$\nu=\frac{3\times 10^8m/s}{0.05m}=6\times 10^{9}s^{-1}$

Therefore, the frequency of the radiation will be, $6\times 10^9s^{-1}$

Answer 2

Answer : The frequency of the radiation will be, 6\times 10^9s^{-1}6×10

9

s

−1

Solution : Given,

Wave number of radiation = 20m^{-1}20m

−1

First we have to calculate the wavelength of radiation.

Formula used : \lambda=\frac{1}{\bar{\nu }}λ=

ν

ˉ

1

where,

\lambdaλ = wavelength of radiation

\bar{\nu }

ν

ˉ

= wave number of radiation

Now put all the given values in this formula, we get

\lambda=\frac{1}{20m^{-1}}=0.05mλ=

20m

−1

1

=0.05m

Now we have to calculate the frequency of radiation.

Formula used : \nu=\frac{c}{\lambda}ν=

λ

c

where,

\nuν = frequency of radiation

\lambdaλ = wavelength of radiation

c = speed of light = 3\times 10^8m/s3×10

8

m/s

Now put all the given values in this formula, we get

\nu=\frac{3\times 10^8m/s}{0.05m}=6\times 10^{9}s^{-1}ν=

0.05m

3×10

8

m/s

=6×10

9

s

−1

Therefore, the frequency of the radiation will be, 6\times 10^9s^{-1}6×10

9

s

−1