Answer
a. $265$ nm
b. Yes
c. Copper
Work Step by Step
a. To find the wavelength of the photon needed to eject an electron, we can use the equation:
\[ \lambda = \frac{hc}{E} \]
Where:
\( \lambda \) = wavelength of the photon
\( h \) = Planck's constant (\( 6.626 \times 10^{-34} \mathrm{~J\cdot s} \))
\( c \) = speed of light in a vacuum (\( 3.00 \times 10^{8} \mathrm{~m/s} \))
\( E \) = energy of the photon
The energy of the photon needed to eject an electron is equal to the work function of the hull, so \( E = 7.52 \times 10^{-19} \mathrm{~J} \).
Plugging in the values, we get:
\[ \lambda = \frac{(6.626 \times 10^{-34} \mathrm{~J\cdot s})(3.00 \times 10^{8} \mathrm{~m/s})}{7.52 \times 10^{-19} \mathrm{~J}} \]
Solving for \( \lambda \), we find:
\[ \lambda \approx 2.65 \times 10^{-7} \mathrm{~m} \]
So, the wavelength of the photon needed to eject an electron is approximately \( 265 \mathrm{~nm} \).
b. The given photon torpedo has a wavelength of \( 259 \mathrm{~nm} = 259 \times 10^{-9} \mathrm{~m} \). Comparing this to the wavelength we calculated in part a ($259<265$), we find that the given photon torpedo has sufficient energy to eject an electron. So, yes, 259-nm electromagnetic radiation will eject an electron.
c. The element with an electron configuration of copper (Cu).
