Question

1. What is the frequency in hertz of a photon that has a wavelength of 5.78 x 104 m? 2. Calculate the wavelength of a wave that has a frequency of 22.4 MHz.
3. What is the frequency in hertz of a photon that has a wavelength of 67.9 m?
4. Calculate the wavelength of a wave that has a frequency of 34.66 Hz.
5. What is the frequency in hertz of a photon that has a wavelength of 9.98 mm?

Answer 1

Answer :

Solution For 1 :

Given,

wavelength = $5.78\times 10^4m$

Speed of light = $2.998\times 10^{8}m/s$

Formula used :

$\nu=\frac{c}{\lambda}$           .............(1)

$\nu$ = frequency

$\lambda$ = wavelength

c = speed of light

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

$\nu=\frac{2.998\times 10^8m/s}{5.78\times 10^{4}m}=0.5185\times 10^{4}s^-=5.185\times 10^{3}s^-$ = $5.185\times 10^{3}Hz$  

(1Hz = 1 per second)

Therefore, the frequency of a photon in hertz is $5.185\times 10^{3}Hz$.

Solution For 2 :

Given,

Frequency = $22.4MHz=22.4\times 10^6Hz$       $(1MHz=10^6Hz)$

Speed of light = $2.998\times 10^{8}m/s$

Now put all the given values in above formula (1), we get

$\lambda=\frac{2.998\times 10^8m/s}{22.4\times 10^{6}s^-}=0.1338\times 10^{2}m=13.38m$

Therefore, the wavelength of a wave is 13.38 m.

Solution For 3 :

Given,

wavelength = $67.9m$

Speed of light = $2.998\times 10^{8}m/s$

Now put all the given values in above formula (1), we get

$\nu=\frac{2.998\times 10^8m/s}{67.9m}=0.04415\times 10^{8}s^-=4.415\times 10^{6}s^-$ = $4.415\times 10^{6}Hz$

Therefore, the frequency of a photon in hertz is $4.415\times 10^{6}Hz$.

Solution For 4 :

Given,

Frequency = $34.66Hz$

Speed of light = $2.998\times 10^{8}m/s$

Now put all the given values in above formula (1), we get

$\lambda=\frac{2.998\times 10^8m/s}{34.66s^-}=0.08649\times 10^{8}m=86.49\times 10^5m$          

Therefore, the wavelength of a wave is $86.49\times 10^5m$.

Solution For 5 :

Given,

wavelength = $9.98mm=9.98\times 10^{-3}m$      (1 m  = 1000 mm)

Speed of light = $2.998\times 10^{8}m/s$

Now put all the given values in above formula (1), we get

$\nu=\frac{2.998\times 10^8m/s}{9.98\times 10^{-3}m}=0.3004\times 10^{11}s^-=3.004\times 10^{10}s^-$ = $3.004\times 10^{10}Hz$

Therefore, the frequency of a photon in hertz is $5.185\times 10^{3}Hz$.