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 $h$ is Planck's constant ($h=6.63\times 10^{-34}\ J\cdot s$) and $
u$ is the frequency of the light. Since $h$ is a constant, the energy $E$ is directly proportional to the frequency $
u$.

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 frequency $
u_3 = 1.4\times 10^{15}\ s^{-1}$ is the highest.

Answer:

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