Can someone help me figure out the wavelength of a gamma ray with a frequency of 1.0 x 10^19 Hz?

Question

I can't figure it out, have tried and tried. I know that c + 3.0 x 10^8 Hz,

What I can't figure out isw what the two question marks are in ? x 10 ^ ? m

I thought it was 3, -9

Any help would be appreciated. I have had it.

Answer 1

frequency is the inverse of the period multiplied by velocity, f=v/lambda,

period or wave length is the inverse of the frequency multiplied by velocity

velocity = c = about 3 x 10^8 m/s

wave length = lambda =v/f = about 3 x10^8/10^-19

wave length = the period = lambda as the Greek symbol

velocity = 2.99792458 m/sec = about 3 x 10^8 m/s

frequency = 10^19 Hz = cycles per second

wave length = about 3 x 10^8 divided by 10^19 = 3 x 10^(8-19) = 3 x 10^-11 meters

gamma wave length = 3 x 10^-11 meters

(gamma ray wave lengths actually vary, estimated at 3x 10^-10 to 3x 10^-14,

mostly about 3 x 10^-12. 3 x 10^-11 is in the general range)

a pico meter, pm is one trillionth of a meter. 1 meter = 1 trillion pm = a million million pm = 10^^-6 x 10^-6 = 10^-12 pm

so you might convert the meters into pico meters

Answer 2

You can use:

Lambda= v/f

Where lambda stands for wavelength.

Plug in your terms and solve. The velocity or speed of light constant is 3.0×10^8.m/s

Lambda=(3.0×10^8m/s)/1.0×10^19Hz or s^-1

Because Hz and s^-1 are the same expression.

Lambda or wavelength = 3.0×10^-11 m.