Question

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

Answer 1

To find:

Wavelength and frequency of 100 MeV photon?

Calculation:

Let frequency be f and wavelength of $\lambda$:

$\sf \therefore \: hf = energy$

$\sf \implies \: 6.63 \times {10}^{ - 34} \times f = 100 \times {10}^{6} \times( 1.6 \times {10}^{ - 19} )$

$\sf \implies \: 6.63 \times {10}^{ - 34} \times f = {10}^{8} \times( 1.6 \times {10}^{ - 19} )$

$\sf \implies \: 6.63 \times {10}^{ - 34} \times f = 1.6 \times {10}^{ - 11}$

$\sf \implies \: f = \dfrac{1.6}{6.63} \times {10}^{ - 11 + 34}$

$\sf \implies \: f = 0.24\times {10}^{ 23}$

$\boxed{ \sf \implies \: f = 24\times {10}^{ 21} \: hz}$

$\sf \implies \: \lambda= \dfrac{3 \times {10}^{8} }{24\times {10}^{ 21}}$

$\sf \implies \: \lambda= \dfrac{ {10}^{8} }{8\times {10}^{ 21}}$

$\boxed{ \sf \implies \: \lambda= 0.125 \times {10}^{ - 13} \: m}$

Answer 2

Explanation:

To find:

Wavelength and frequency of 100 MeV photon?

Calculation:

Let frequency be f and wavelength of \lambdaλ :

\sf \therefore \: hf = energy∴hf=energy

\sf \implies \: 6.63 \times {10}^{ - 34} \times f = 100 \times {10}^{6} \times( 1.6 \times {10}^{ - 19} )⟹6.63×10

−34

×f=100×10

6

×(1.6×10

−19

)

\sf \implies \: 6.63 \times {10}^{ - 34} \times f = {10}^{8} \times( 1.6 \times {10}^{ - 19} )⟹6.63×10

−34

×f=10

8

×(1.6×10

−19

)

\sf \implies \: 6.63 \times {10}^{ - 34} \times f = 1.6 \times {10}^{ - 11} ⟹6.63×10

−34

×f=1.6×10

−11

\sf \implies \: f = \dfrac{1.6}{6.63} \times {10}^{ - 11 + 34} ⟹f=

6.63

1.6

×10

−11+34

\sf \implies \: f = 0.24\times {10}^{ 23} ⟹f=0.24×10

23

\boxed{ \sf \implies \: f = 24\times {10}^{ 21} \: hz}

⟹f=24×10

21

hz

\sf \implies \: \lambda= \dfrac{3 \times {10}^{8} }{24\times {10}^{ 21}} ⟹λ=

24×10

21

3×10

8

\sf \implies \: \lambda= \dfrac{ {10}^{8} }{8\times {10}^{ 21}} ⟹λ=

8×10

21

10

8

\boxed{ \sf \implies \: \lambda= 0.125 \times {10}^{ - 13} \: m}

⟹λ=0.125×10

−13

m