Question

calculate the energy in joules per photon of an x - ray with a wavelength of 88.8nm
a) 2.24×10^(-18) j/photon
b) 4.75×10^(-19) j/photon
c) 1.37×10^(-15) j/photon
d) 3.09×10^(-20) j/photon
e) 1.52×10^(-16) j/photon

Explanation:

Step1: Recall the energy - wavelength formula

The energy of a photon is given by $E = \frac{hc}{\lambda}$, where $h = 6.626\times10^{-34}\ J\cdot s$ (Planck's constant), $c= 3.0\times 10^{8}\ m/s$ (speed of light) and $\lambda$ is the wavelength. First, convert the wavelength from nanometers to meters. Given $\lambda = 88.8\ nm=88.8\times 10^{-9}\ m$.

Step2: Substitute the values into the formula

$E=\frac{6.626\times 10^{-34}\ J\cdot s\times3.0\times 10^{8}\ m/s}{88.8\times 10^{-9}\ m}$.
First, calculate the numerator: $6.626\times 10^{-34}\times3.0\times 10^{8}=19.878\times 10^{-26}\ J\cdot m$.
Then, divide by the denominator: $E=\frac{19.878\times 10^{-26}\ J\cdot m}{88.8\times 10^{-9}\ m}\approx2.24\times 10^{-18}\ J$.

Answer:

a) $2.24\times 10^{-18}\ J$/photon