45. What is the frequency of a gamma wave with a wavelength of $$ 1.2 imes 10^{-14} \mathrm{~m} $$ ?

Question

45. What is the frequency of a gamma wave with a wavelength of $$ 1.2 	imes 10^{-14} \mathrm{~m} $$ ?

UpStudy AI · Accepted Answer

The relationship between the speed of light, wavelength, and frequency is given by

$$
c = \lambda f,
$$

where $$ c $$ is the speed of light, $$ \lambda $$ is the wavelength, and $$ f $$ is the frequency.

**Step 1:** Solve for frequency

$$
f = \frac{c}{\lambda}.
$$

**Step 2:** Substitute the given values

Using $$ c \approx 3.00 \times 10^8 \, \mathrm{m/s} $$ and $$ \lambda = 1.2 \times 10^{-14} \, \mathrm{m} $$,

$$
f = \frac{3.00 \times 10^8 \, \mathrm{m/s}}{1.2 \times 10^{-14} \, \mathrm{m}}.
$$

**Step 3:** Perform the division

Divide the coefficients:

$$
\frac{3.00}{1.2} = 2.5.
$$

Add the exponents of 10:

$$
10^8 \div 10^{-14} = 10^{8 - (-14)} = 10^{22}.
$$

Thus,

$$
f = 2.5 \times 10^{22} \, \mathrm{Hz}.
$$
The frequency of the gamma wave is $$ 2.5 \times 10^{22} \, \mathrm{Hz} $$.

45. What is the frequency of a gamma wave with a wavelength of \( 1.2 \times 10^{-14} \mathrm{~m} \) ?