Question

find the wavelength and frequency of a 100-MeV photon​

Answer 1

GIVEN

• Energy of Photon → 100-MeV

TO FIND

• Frequency
• Wavelength

SOLUTION

• Let frequency be f and wavelength of λ

USED FORMULA

• Energy = hf [h = Plank′s constant]
• λ = c / f [c = speed of light]

• Energy = hf
• 6.63 × 10-³⁴ × f = 100×10⁶ × (1.6×10-¹⁹)
• f = 0.24 × 10²³
• f = 24 × 10²¹ H

• λ = c / f
• λ = (3 × 10⁸) / (24 × 10²¹)
• λ = 0.125 × 10-¹³ m

Answer 2

Concept:

We need to apply the energy equation, E = hf where f can be represented as, f = c/λ

Given:

Energy of photon = 100 MeV

Find:

We need to determine:

Wavelength, λ  and Frequency, f of a photon.

Solution:

We know the equation gives the energy of a photon-

E = hf, where h is the Planck constant, f is the frequency, and E is the energy.

We know the frequency, f = c/λ where c is the speed of light and λ is the wavelength

Therefore, the equation of energy becomes-

E = h×c/λ

Therefore, λ = hc/E

We know, h = 6.62 × 10⁻³⁴ and c = 3 × 10⁸

E is given as 100 MeV = 100 × 1.6   10⁻¹³ = 1.6 × 10⁻¹¹

Therefore, λ =  6.62 × 10⁻³⁴ ×  3 × 10⁸/ 1.6 × 10⁻¹¹

λ = 12.4125 × 10⁻¹⁵m

For the frequency, the equation becomes-

E = hf

Therefore, f = E/h

f = 1.6 × 10⁻¹¹ / 6.62 × 10⁻³⁴

f = 0.2416 × 10²³ = 2.416 × 10²² Hz

Thus, the wavelength and frequency of 100 MeV photons are 12.4125 × 10⁻¹⁵ m and 2.416 × 10²² Hz, respectively.

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