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

Solution For 1 :

Given,

wavelength =
`5.78* 10^4m`

Speed of light =
`2.998* 10^(8)m/s`

Formula used :

`\\u=(c)/(\lambda)` .............(1)

`\\u` = frequency

`\lambda` = wavelength

c = speed of light

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

`\\u=(2.998* 10^8m/s)/(5.78* 10^(4)m)=0.5185* 10^(4)s^-=5.185* 10^(3)s^-` =
`5.185* 10^(3)Hz`

(1Hz = 1 per second)

Therefore, the frequency of a photon in hertz is
`5.185* 10^(3)Hz`.

Solution For 2 :

Given,

Frequency =
`22.4MHz=22.4* 10^6Hz`
`(1MHz=10^6Hz)`

Speed of light =
`2.998* 10^(8)m/s`

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

`\lambda=(2.998* 10^8m/s)/(22.4* 10^(6)s^-)=0.1338* 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* 10^(8)m/s`

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

`\\u=(2.998* 10^8m/s)/(67.9m)=0.04415* 10^(8)s^-=4.415* 10^(6)s^-` =
`4.415* 10^(6)Hz`

Therefore, the frequency of a photon in hertz is
`4.415* 10^(6)Hz`.

Solution For 4 :

Given,

Frequency =
`34.66Hz`

Speed of light =
`2.998* 10^(8)m/s`

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

`\lambda=(2.998* 10^8m/s)/(34.66s^-)=0.08649* 10^(8)m=86.49* 10^5m`

Therefore, the wavelength of a wave is
`86.49* 10^5m`.

Solution For 5 :

Given,

wavelength =
`9.98mm=9.98* 10^(-3)m` (1 m = 1000 mm)

Speed of light =
`2.998* 10^(8)m/s`

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

`\\u=(2.998* 10^8m/s)/(9.98* 10^(-3)m)=0.3004* 10^(11)s^-=3.004* 10^(10)s^-` =
`3.004* 10^(10)Hz`

Therefore, the frequency of a photon in hertz is
`5.185* 10^(3)Hz`.