Question

chemistry worksheet - wavelength, frequency, & energy of electromagnetic waves. show all equations, work, units, and significant figures in performing the following calculations. identify the type of radiation in each problem (use your electromagnetic spectrum) c = λv e = hv c = 3.00×10⁸ m/s h = 6.6262×10⁻³⁴ j - s (or j/hz) 1. what is the wavelength of a wave having a frequency of 3.76×10¹⁴ s⁻¹? 2. what is the frequency of a 6.9×10⁻¹³ m wave? 3. what is the wavelength of a 2.99 hz wave? 4. what is the wavelength of a 1.28×10¹⁷ hz wave? 5. what is the frequency of a 7.43×10⁻⁵ m wave? 6. what is the frequency of a 2,600 cm wave? 7. what is the wavelength of a 4.34×10¹⁵ /s wave? 8. what is the wavelength of 109.6 mhz wave? 9. calculate the wavelength of the electromagnetic radiation whose frequency is 7.500×10¹² hz. 10. determine the frequency of light whose wavelength is 4.257×10⁻⁷ cm.

Explanation:

Step1: Recall the speed - wavelength - frequency formula

The formula is $c = \lambda
u$, where $c = 3.00\times 10^{8}\text{ m/s}$, $\lambda$ is the wavelength and $
u$ is the frequency. We can re - arrange it to solve for $\lambda=\frac{c}{
u}$ and $
u=\frac{c}{\lambda}$.

1.

Step1: Identify the given values

Given $
u = 3.76\times 10^{14}\text{ s}^{-1}$, $c = 3.00\times 10^{8}\text{ m/s}$.

Step2: Calculate the wavelength

$\lambda=\frac{c}{
u}=\frac{3.00\times 10^{8}\text{ m/s}}{3.76\times 10^{14}\text{ s}^{-1}}\approx7.98\times 10^{-7}\text{ m}$

2.

Step1: Identify the given values

Given $\lambda = 6.9\times 10^{-13}\text{ m}$, $c = 3.00\times 10^{8}\text{ m/s}$.

Step2: Calculate the frequency

$
u=\frac{c}{\lambda}=\frac{3.00\times 10^{8}\text{ m/s}}{6.9\times 10^{-13}\text{ m}}\approx4.35\times 10^{20}\text{ Hz}$

3.

Step1: Identify the given values

Given $
u = 2.99\text{ Hz}$, $c = 3.00\times 10^{8}\text{ m/s}$.

Step2: Calculate the wavelength

$\lambda=\frac{c}{
u}=\frac{3.00\times 10^{8}\text{ m/s}}{2.99\text{ Hz}}\approx1.00\times 10^{8}\text{ m}$

4.

Step1: Identify the given values

Given $
u = 1.28\times 10^{17}\text{ Hz}$, $c = 3.00\times 10^{8}\text{ m/s}$.

Step2: Calculate the wavelength

$\lambda=\frac{c}{
u}=\frac{3.00\times 10^{8}\text{ m/s}}{1.28\times 10^{17}\text{ Hz}}\approx2.34\times 10^{-9}\text{ m}$

5.

Step1: Identify the given values

Given $\lambda = 7.43\times 10^{-9}\text{ m}$, $c = 3.00\times 10^{8}\text{ m/s}$.

Step2: Calculate the frequency

$
u=\frac{c}{\lambda}=\frac{3.00\times 10^{8}\text{ m/s}}{7.43\times 10^{-9}\text{ m}}\approx4.04\times 10^{16}\text{ Hz}$

6.

First, convert $2600\text{ cm}$ to meters: $2600\text{ cm}=26\text{ m}$.

Step1: Identify the given values

Given $\lambda = 26\text{ m}$, $c = 3.00\times 10^{8}\text{ m/s}$.

Step2: Calculate the frequency

$
u=\frac{c}{\lambda}=\frac{3.00\times 10^{8}\text{ m/s}}{26\text{ m}}\approx1.15\times 10^{7}\text{ Hz}$

7.

Step1: Identify the given values

Given $
u = 4.34\times 10^{15}\text{ s}^{-1}$, $c = 3.00\times 10^{8}\text{ m/s}$.

Step2: Calculate the wavelength

$\lambda=\frac{c}{
u}=\frac{3.00\times 10^{8}\text{ m/s}}{4.34\times 10^{15}\text{ s}^{-1}}\approx6.91\times 10^{-8}\text{ m}$

8.

Convert $109.6\text{ MHz}$ to Hz: $109.6\text{ MHz}=1.096\times 10^{8}\text{ Hz}$

Step1: Identify the given values

Given $
u = 1.096\times 10^{8}\text{ Hz}$, $c = 3.00\times 10^{8}\text{ m/s}$.

Step2: Calculate the wavelength

$\lambda=\frac{c}{
u}=\frac{3.00\times 10^{8}\text{ m/s}}{1.096\times 10^{8}\text{ Hz}}\approx2.74\text{ m}$

9.

Convert $4.257\times 10^{-7}\text{ cm}$ to meters: $4.257\times 10^{-7}\text{ cm}=4.257\times 10^{-9}\text{ m}$

Step1: Identify the given values

Given $\lambda = 4.257\times 10^{-9}\text{ m}$, $c = 3.00\times 10^{8}\text{ m/s}$.

Step2: Calculate the frequency

$
u=\frac{c}{\lambda}=\frac{3.00\times 10^{8}\text{ m/s}}{4.257\times 10^{-9}\text{ m}}\approx7.05\times 10^{16}\text{ Hz}$

10.

Step1: Identify the given values

Given $\lambda = 4.257\times 10^{-7}\text{ cm}=4.257\times 10^{-9}\text{ m}$, $c = 3.00\times 10^{8}\text{ m/s}$.

Step2: Calculate the frequency

$
u=\frac{c}{\lambda}=\frac{3.00\times 10^{8}\text{ m/s}}{4.257\times 10^{-9}\text{ m}}\approx7.05\times 10^{16}\text{ Hz}$

Answer:

1. $\lambda\approx7.98\times 10^{-7}\text{ m}$
2. $

u\approx4.35\times 10^{20}\text{ Hz}$

1. $\lambda\approx1.00\times 10^{8}\text{ m}$
2. $\lambda\approx2.34\times 10^{-9}\text{ m}$
3. $

u\approx4.04\times 10^{16}\text{ Hz}$

1. $

u\approx1.15\times 10^{7}\text{ Hz}$

1. $\lambda\approx6.91\times 10^{-8}\text{ m}$
2. $\lambda\approx2.74\text{ m}$
3. $

u\approx7.05\times 10^{16}\text{ Hz}$

1. $

u\approx7.05\times 10^{16}\text{ Hz}$