Question

If Photon Energy is 6.6 x10^20 J, what is true about EM radiation? (useful quantities: h=6.6 X 10^-34 J s , and c=3.0 X 10^8 m/s

How did you come up with your answer?

Answer 1

Answer on Question #57578, Physics / Mechanics | Relativity

If Photon Energy is $6.6 \times 10^{20} \, \text{J}$, what is true about EM radiation? (useful quantities: $h = 6.6 \times 10^{-34} \, \text{J} \, \text{s}$, and $c = 3.0 \times 10^{-8} \, \text{m/s}$? How did you come up with your answer?

Find: $\lambda - ?$

Given:

$$E = 6,6 \times 10^{20} \, \text{J}$$ $$h = 6,6 \times 10^{-34} \, \text{J} \times \text{s}$$ $$c = 3 \times 10^{8} \, \text{m/s}$$

Solution:

The energy of Photon:

$$E = h \upsilon \, (1),$$

where $h$ – Planck’s constant,

$\upsilon$ – frequency of electromagnetic radiation

The wave length of the electromagnetic radiation:

$$\lambda = c T \, (2),$$

where $c$ – speed of light,

$T$ – period of oscillation

Period of oscillation and frequency electromagnetic radiation are related of ratio:

$$T = \frac{1}{\upsilon} \, (3)$$

(3) in (2): $\lambda = \frac{c}{\upsilon} \, (4)$

Of (4) $\Rightarrow \upsilon = \frac{c}{\lambda} \, (5)$

(5) in (1): $E = \frac{hc}{\lambda} \, (6)$

Of (6) $\Rightarrow \lambda = \frac{hc}{E} \, (7)$

Of (7) $\Rightarrow \lambda = 3 \times 10^{-46} \, \text{m}$

The smallest wave length have $\gamma$-radiation ($\lambda = 10^{-10} \, \text{m} - 10^{-13} \, \text{m}$).

Electromagnetic radiation with length wave $\lambda = 3 \times 10^{-46} \, \text{m}$ does not exist.

Answer:

It is not true.

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