Question

(b) the energy

(c) the region of the em spectrum/type of radiation

6.) a photon has an energy of 4.00 x 10^(-19) j. find...
(a) the frequency
(b) the wavelength

(d) the region of the em spectrum/type of radiation

7.) a bright line spectrum contains a line with a wavelength of 518 nm. determine...
(a) the wavelength in meters

(b) the frequency

(c) the energy

(d) the color

8.) cobalt - 60 is an artificial radioisotope that is produced in a nuclear reactor for use as a gamma ray source in the treatment of certain types of cancer. if the wavelength of the gamma radiation from a cobalt - 60 source is 1.00 x 10^(-3) nm, calculate the energy of a photon of this radiation.

Explanation:

Problem 6

Step1: Find the frequency

Use the formula $E = h
u$, where $E$ is energy, $h = 6.63\times10^{- 34}\ J\cdot s$ (Planck's constant) and $
u$ is frequency. Rearranging for $
u$ gives $
u=\frac{E}{h}$.
$
u=\frac{4.00\times 10^{-19}\ J}{6.63\times10^{-34}\ J\cdot s}\approx6.03\times 10^{14}\ Hz$

Step2: Find the wavelength

Use the formula $c=\lambda
u$, where $c = 3.00\times10^{8}\ m/s$ (speed of light in vacuum), $\lambda$ is wavelength and $
u$ is frequency. Rearranging for $\lambda$ gives $\lambda=\frac{c}{
u}$.
$\lambda=\frac{3.00\times 10^{8}\ m/s}{6.03\times 10^{14}\ Hz}\approx4.98\times 10^{-7}\ m = 498\ nm$

Step3: Determine the region of the EM - spectrum

Since the wavelength is $498\ nm$, this is in the visible light region. Specifically, it is in the blue - green part of the visible spectrum.

Step1: Convert wavelength to meters

Given $\lambda = 518\ nm$. Since $1\ nm=1\times10^{-9}\ m$, then $\lambda=518\times10^{-9}\ m = 5.18\times 10^{-7}\ m$

Step2: Find the frequency

Use $c = \lambda
u$, so $
u=\frac{c}{\lambda}$.
$
u=\frac{3.00\times 10^{8}\ m/s}{5.18\times 10^{-7}\ m}\approx5.79\times 10^{14}\ Hz$

Step3: Calculate the energy

Use $E = h
u$, with $h = 6.63\times10^{-34}\ J\cdot s$ and $
u = 5.79\times 10^{14}\ Hz$.
$E=6.63\times10^{-34}\ J\cdot s\times5.79\times 10^{14}\ Hz\approx3.84\times 10^{-19}\ J$

Step4: Determine the color

A wavelength of $518\ nm$ corresponds to green light in the visible spectrum.

Step1: Convert wavelength to meters

Given $\lambda = 1.00\times10^{-3}\ nm$. Since $1\ nm = 1\times10^{-9}\ m$, then $\lambda=1.00\times10^{-3}\times10^{-9}\ m=1.00\times 10^{-12}\ m$

Step2: Find the frequency

Use $c=\lambda
u$, so $
u=\frac{c}{\lambda}$.
$
u=\frac{3.00\times 10^{8}\ m/s}{1.00\times 10^{-12}\ m}=3.00\times 10^{20}\ Hz$

Step3: Calculate the energy

Use $E = h
u$, with $h = 6.63\times10^{-34}\ J\cdot s$ and $
u = 3.00\times 10^{20}\ Hz$.
$E=6.63\times10^{-34}\ J\cdot s\times3.00\times 10^{20}\ Hz = 1.99\times 10^{-13}\ J$

Answer:

(A) $6.03\times 10^{14}\ Hz$
(B) $498\ nm$
(D) Visible light (blue - green)

Problem 7