Question

Violet light has a frequency of 7.26 × 10^14 Hz and travels at a speed of 3.00 × 10^8 m/s. HINT: to convert to nanometers (nm) multiply your final answer by 10^9. *

1 point
Captionless Image
2.18 x 10^32 nm
413 nm
2.42 x10^15
0.00242

Answer 1

413 nm

Step-by-step explanation:

The wavelength is defined as

`\lambda = (c)/(f)`

Where
`\lambda` represents the wavelength,
`c` the speed of the wave which is a constant and
`f` is the frequency of the wave,

In this case, we know

`c = 3.00 * 10^(8) m/s`

`f=7.26 * 10^(14)Hz`, where
`Hz=(1)/(sec)`

Replacing these given values in the formula, we have

`\lambda= (3.00 * 10^(8) m/s )/(7.26* 10^(14) (1)/(sec) )\\ \lambda = 0.4132 * 10^(-6) m`

But, we know that
`1 \ m = 10^(9) \ nm`

So, we use the equivalence to transform the wavelength from meters to nanometers.

`0.4132 * 10^(-6)m(10^(9)nm )/(1m) =0.4132 * 10^(3) \ nm=413.2 nm`

Therefore, the wavelength is 413.2 nanometers, approximately.