Answer:
1.69 x 10 ²⁰ Hz
1.77 x 10⁻¹² m
Explanation:
For any radiation, its energy is give by
E= hν = h c/λ where
h= Planck's constant ,
ν = Frequency,
λ = wavelength,
c= speed of light
We have all the information so plug the values, being careful with the units.
E = h ν∴ ν = E/h
= (0.700 MeV x 1x10⁶ eV/MeV x 1.602 x 10⁻¹⁹ J/eV ) / 6.626 x 10⁻³⁴ J s
= 1.69 x 10 ²⁰ s⁻¹ = 1.69 x 10 ²⁰ Hz ( 1 Hz = 1s⁻¹)
λ = c/ ν = (3 x 10^8 m/s) / 1.69 x 10 ²⁰ s⁻¹ = 1.77 x 10⁻¹² m
The frequency of the gamma photon is 1.87 × 10^20 Hz and its wavelength is 1.6 × 10^-14 m.
Given that; 1 eV = 1.602 × 10−19 J
0.700 MeV = 0.700 × 10^6 eV
If 1 eV = 1.602 × 10−19 J
0.700 × 10^6 eV = 0.700 × 10^6 eV × 1.602 × 10−19 J/1 eV
= 1.12 × 10^-13 J
Since E = hf
Where;
E = energy of the gamma photon = 1.12 × 10^-13 J
h = Plank's constant = 6 × 10^-34 Js
f = ?
f = E/h
f = 1.12 × 10^-13 J/ 6 × 10^-34 Js
f = 1.87 × 10^20 Hz
c = λf
Where
c = speed of light = 3 × 10^8 m/s
λ = wavelength = ?
f = frequency = 1.87 × 10^20 Hz
λ = c/f
λ = 3 × 10^8 m/s/1.87 × 10^20 Hz
λ = 1.6 × 10^-12 m
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