Question

which of the following frequencies of light has the highest energy?
5.0 x 10^14 s^-1
7.0 x 10^13 s^-1
1.4 x 10^15 s^-1
2.3 x 10^14 s^-1
2.5 x 10^10 s^-1

Explanation:

Step1: Recall energy - frequency formula

The energy of a photon is given by $E = h
u$, where $E$ is energy, $h$ is Planck's constant ($h=6.626\times 10^{-34}\ J\cdot s$) and $
u$ is frequency. Since $h$ is a constant, the higher the frequency $
u$, the higher the energy $E$.

Step2: Compare the given frequencies

We have the following frequencies: $
u_1 = 5.0\times 10^{14}\ s^{-1}$, $
u_2=7.0\times 10^{13}\ s^{-1}$, $
u_3 = 1.4\times 10^{15}\ s^{-1}$, $
u_4=2.3\times 10^{14}\ s^{-1}$, $
u_5 = 2.5\times 10^{10}\ s^{-1}$.
Comparing the exponents of 10 in each frequency value:

• For $

u_1$, the exponent is 14.

• For $

u_2$, the exponent is 13.

• For $

u_3$, the exponent is 15.

• For $

u_4$, the exponent is 14.

• For $

u_5$, the exponent is 10.
Since $15>14 > 13>10$, the highest - frequency value is $
u_3 = 1.4\times 10^{15}\ s^{-1}$.

Answer:

$1.4\times 10^{15}\ s^{-1}$