4. Calculate the photon's mass if its frequency is equal to $$ 6 imes 10^{\wedge} 15 \mathrm{~Hz} $$

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4. Calculate the photon's mass if its frequency is equal to $$ 6 	imes 10^{\wedge} 15 \mathrm{~Hz} $$

UpStudy AI · Accepted Answer

1. The energy of a photon is given by the formula  
   $$
   E = h f,
   $$  
   where $$ h $$ is Planck's constant and $$ f $$ is the frequency of the photon.

2. For the given frequency,  
   $$
   f = 6 \times 10^{15} \, \mathrm{Hz},
   $$  
   and Planck's constant is  
   $$
   h \approx 6.626 \times 10^{-34} \, \mathrm{J \cdot s}.
   $$

3. The energy of the photon is then  
   $$
   E = \left(6.626 \times 10^{-34}\right) \left(6 \times 10^{15}\right) = 3.9756 \times 10^{-18} \, \mathrm{J}.
   $$

4. According to Einstein's relation between energy and mass:  
   $$
   E = m c^2,
   $$  
   where $$ c $$ is the speed of light $$\left(c \approx 3 \times 10^8 \, \mathrm{m/s}\right)$$. Solving for the mass $$ m $$, we get  
   $$
   m = \frac{E}{c^2}.
   $$

5. Substituting in the values,  
   $$
   m = \frac{3.9756 \times 10^{-18}}{(3 \times 10^8)^2} = \frac{3.9756 \times 10^{-18}}{9 \times 10^{16}}.
   $$

6. Simplify the expression:  
   $$
   m = \frac{3.9756}{9} \times 10^{-18 - 16} = 0.44173 \times 10^{-34} \, \mathrm{kg}.
   $$

7. Expressing with one digit before the decimal:  
   $$
   m \approx 4.42 \times 10^{-35} \, \mathrm{kg}.
   $$

Thus, the photon's mass is approximately  
$$
4.42 \times 10^{-35} \, \mathrm{kg}.
$$
The photon's mass is approximately $$ 4.42 \times 10^{-35} $$ kilograms.

Calculate the photon’s mass if its frequency is equal to

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