What is the wavelength of a photon with a frequency of 7.81 1014 Hz? A.
517 nm

B.
384 nm

C.
848 nm

D.
234 nm

Option B. 384 nm

Explanation:

From the question given above, the following data were obtained:

Frequency (f) = 7.81×10¹⁴ Hz

Velocity of photon (v) = 3×10⁸ m/s

Wavelength (λ) =?

The wavelength of the photon can be obtained as follow:

v = λf

3×10⁸ = λ × 7.81×10¹⁴

Divide both side by 7.81×10¹⁴

λ = 3×10⁸ / 7.81×10¹⁴

λ = 3.84×10¯⁷ m

Finally, we shall convert 3.84×10¯⁷ M to nm. This can be obtained as follow:

1×10¯⁹ m = 1 nm

Therefore,

3.84×10¯⁷ m = 3.84×10¯⁷ m × 1 nm / 1×10¯⁹ m

3.84×10¯⁷ m = 384 nm

Thus, the wavelength of the photon is 384 nm

in scientific notation, the value of the  speed of light in a vacuum

  will be written as 2.995 * 10^8. when this value is represented in the form of

  a * 10^b, then, a = 2.995 and b = 8.

the value of the speed of light in a vacuum given above can also be rounded up to approximately 300000000. in this case, the scientific notation will be written as 3 *10^8.