Question

1. what is the energy of a photon of light with a frequency of 3.12 x 10¹⁴ hz? 16. what is the frequency of a 1.78 x 10⁻¹⁵ j photon of light?

Explanation:

Step1: Recall the energy - frequency formula

The energy of a photon is given by the formula $E = h
u$, where $E$ is the energy of the photon, $h$ is Planck's constant ($h=6.63\times 10^{-34}\ J\cdot s$), and $
u$ is the frequency of the photon.

Question 15

Step1: Identify the given values

The frequency of the photon is $
u = 3.12\times 10^{14}\ Hz$.

Step2: Calculate the energy

Using the formula $E = h
u$, we substitute $h = 6.63\times 10^{-34}\ J\cdot s$ and $
u=3.12\times 10^{14}\ Hz$.
$E=(6.63\times 10^{-34}\ J\cdot s)\times(3.12\times 10^{14}\ Hz)$
$E = 6.63\times3.12\times 10^{-34 + 14}\ J$
$E=20.6856\times 10^{-20}\ J$
$E = 2.07\times 10^{-19}\ J$

Question 16

Step1: Rearrange the energy - frequency formula

We have $E = h
u$, so $
u=\frac{E}{h}$.

Step2: Identify the given values

The energy of the photon is $E = 1.78\times 10^{-15}\ J$ and $h = 6.63\times 10^{-34}\ J\cdot s$.

Step3: Calculate the frequency

$
u=\frac{1.78\times 10^{-15}\ J}{6.63\times 10^{-34}\ J\cdot s}$
$
u=\frac{1.78}{6.63}\times10^{-15+ 34}\ Hz$
$
u = 0.2684766\times10^{19}\ Hz$
$
u=2.68\times 10^{18}\ Hz$

Answer:

1. $2.07\times 10^{-19}\ J$
2. $2.68\times 10^{18}\ Hz$