Question

calculate the total energy in 1.5 x10^13 photons of gamma radiation having lambda = 3.0*10^-12

Answer 1

Answer: 0.99 Joules

Explanation:

The relationship between wavelength and frequency of the wave follows the equation:

$E=\frac{Nhc}{\lambda}$

where,

$E$ = energy of the wave

N = number of photons = $1.5\times 10^{13}$

h = plank constant = $6.6\times 10^{-34}Js^{-1}$

c = speed of light = $3\times 10^8m/s$

$\lambda$ = wavelength of the wave = $3.0\times 10^{-12}m$

Putting all the values:

$E=\frac{1.5\times 10^{13}\times 6.6\times 10^{-34}\times 3\times 10^8m/s}{3.0\times 10^[-12}m}=0.99J$

The total energy in $1.5\times 10^{13}$ photons of gamma radiation having lambda =$3.0\times 10^{-12}m$ is 0.99 Joules

Answer 2

The total energy of the given photons in the radiation is 0.994 J.

The given parameters;

• number of the photons, N = 1.5 x 10¹³

The energy of  a single photon is calculated as follows;

E = hf

$E = h\frac{c}{\lambda}$

where;

• h is Planck's constant = 6.626 x 10⁻³⁴ Js
• c is the speed of light = 3 x 10⁸ m/s
• λ is the wavelength = 3 x 10⁻¹² m

The energy of a photon in the radiation is calculated as;

$E = \frac{hc}{\lambda} = \frac{(6.626\times 10^{-34}) \times (3\times 10^8)}{3\times 10^{-12}} \\\\E = 6.626 \times 10^{-14} \ J/photon$

The total energy of the given photons is calculated as follows;

$E_t = E\times n\\\\E_t = 6.626 \times 10^{-14} \times 1.5\times 10^{13}\\\\E_t = 0.994 \ J$

Thus, the total energy of the given photons in the radiation is 0.994 J.

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