Question

problem 6: an x - ray has an energy of 1.24×10^(-15) j. what is its wavelength in meters?
problem 7: a green laser pointer emits light with a wavelength of 5.32×10^(-7) m. what is the energy of a single photon from this laser in joules?
problem 8: what is the wavelength, in meters, of a photon that has an energy of 3.5×10^(-20) j?
problem 9: a photon of ultraviolet light has an energy of 8.28×10^(-19) j. what is the wavelength of this light in meters
problem 10: a photon of light has a wavelength of 6.0×10^(-7) m. what is its frequency in hz?

Explanation:

Problem 6

Step1: Recall energy - wavelength formula

The energy of a photon is given by $E = \frac{hc}{\lambda}$, where $E$ is energy, $h = 6.63\times10^{-34}\ J\cdot s$ (Planck's constant), $c= 3\times 10^{8}\ m/s$ (speed of light) and $\lambda$ is wavelength. We need to solve for $\lambda$, so $\lambda=\frac{hc}{E}$.

Step2: Substitute values

$\lambda=\frac{6.63\times 10^{-34}\ J\cdot s\times3\times 10^{8}\ m/s}{1.24\times 10^{-15}\ J}$
$\lambda=\frac{19.89\times 10^{-26}}{1.24\times 10^{-15}}\ m$
$\lambda = 1.60\times10^{-10}\ m$

Step1: Use energy - wavelength formula

$E=\frac{hc}{\lambda}$, with $h = 6.63\times10^{-34}\ J\cdot s$, $c = 3\times 10^{8}\ m/s$ and $\lambda=5.32\times 10^{-7}\ m$.

Step2: Substitute values

$E=\frac{6.63\times 10^{-34}\ J\cdot s\times3\times 10^{8}\ m/s}{5.32\times 10^{-7}\ m}$
$E=\frac{19.89\times 10^{-26}}{5.32\times 10^{-7}}\ J$
$E = 3.74\times10^{-19}\ J$

Step1: Rearrange energy - wavelength formula

From $E=\frac{hc}{\lambda}$, we get $\lambda=\frac{hc}{E}$, where $h = 6.63\times10^{-34}\ J\cdot s$, $c = 3\times 10^{8}\ m/s$ and $E = 3.5\times 10^{-20}\ J$.

Step2: Substitute values

$\lambda=\frac{6.63\times 10^{-34}\ J\cdot s\times3\times 10^{8}\ m/s}{3.5\times 10^{-20}\ J}$
$\lambda=\frac{19.89\times 10^{-26}}{3.5\times 10^{-20}}\ m$
$\lambda=5.68\times 10^{-6}\ m$

Answer:

$1.60\times 10^{-10}\ m$

Problem 7