Question

A photon of blue light has a frequency of 7.50 × 10¹⁴ Hz. Calculate the wavelength of this photon (c = 3.00 × 10⁸ m/s) in nanometers. please show work

Answer 1

Answer:

The key to any frequency and wavelength problem is the fact that frequency and wavelength have an inverse relationship described by the equation

λ

⋅

ν

=

c

, where

λ

- the wavelength of the wave

ν

- its frequency

c

- the speed of light in a vacuum, usually given as

3

⋅

10

8

m s

−

1

So, what does an inverse relationship mean?

In simple words, that equation tells you that when frequency increases, wavelength must decrease in order for their product to remain constant.

Likewise, when frequency decreases, wavelength must increase in order for their product to remain constant.

As a consequence of this, you can expect waves that have short wavelengths to also have high frequencies, and waves that have long wavelengths to also have short frequencies.

Explanation:

please mark me brainliest answer

Answer 2

The wavelength of the photon is

Explanation:

• The relation between frequency and wavelength is $\[\nu =\frac{c}{\lambda }\]$ where $\[\nu$ is the frequency, $c$ is the velocity  of light in vaccuum and ${\lambda }$ is the wavelength.

• Given frequency of the photon is $\[7.50\text{ }\times \text{ }10{}^\text{14}\text{ }Hz\]$
• The unit Hertz is the S.I unit of frequency.

• We know that $c=\[3\text{ }\times \text{ }10{}^\text{8}\text{ }m/s\]$

• So,substituting the given values in the above equation we get,$\[\begin{align} & \nu =\frac{c}{\lambda } \\ & 7.50\text{ }\times \text{ }10{}^\text{1}\text{ }Hz=\frac{3\times {{10}^{8}}m/s}{\lambda } \\ & \lambda =\frac{3\times {{10}^{8}}m/s}{7.50\text{ }\times \text{ }10{}^\text{1}\text{ }Hz}=0.4\times {{10}^{-6}}m \\ \end{align}\]$

$\[\begin{align} & \nu =\frac{c}{\lambda } \\ & 7.50\text{ }\times \text{ }10{}^\text{1}\text{ }Hz=\frac{3\times {{10}^{8}}m/s}{\lambda } \\ & \lambda =\frac{3\times {{10}^{8}}m/s}{7.50\text{ }\times \text{ }10{}^\text{1}\text{ }Hz}=0.4\times {{10}^{-6}}m \\ \end{align}\]$$\[\begin{align} & \nu =\frac{c}{\lambda } \\ & 7.50\text{ }\times \text{ }10{}^\text{1}\text{ }Hz=\frac{3\times {{10}^{8}}m/s}{\lambda } \\ & \lambda =\frac{3\times {{10}^{8}}m/s}{7.50\text{ }\times \text{ }10{}^\text{1}\text{ }Hz}=0.4\times {{10}^{-6}}m \\ \end{align}\]$$\nu =\frac{c}{\lambda } \\ \\7.50\text{ }\times \text{ }10{}^\text{14}\text{ }Hz=\frac{3\times {{10}^{8}}m/s}{\lambda } \\ \\& \lambda =\frac{3\times {{10}^{8}}m/s}{7.50\text{ }\times \text{ }10{}^\text{14}\text{ }Hz}=0.4\times {{10}^{-6}}m$

• We got the answer in metres,we need to convert it into nanometres.
• So ,$\[0.4\times {{10}^{-6}}m=400nm\]$.