Answer
\( 2.76 \times 10^{-7} \) meters
Work Step by Step
To find the maximum wavelength of light that can remove an electron from an iron atom, we can use the formula for the energy of a photon:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) J*s),
- \( c \) is the speed of light (\( 3.00 \times 10^8 \) m/s),
- \( \lambda \) is the wavelength of the light.
Rearranging the formula to solve for wavelength (\( \lambda \)), we get:
\[ \lambda = \frac{hc}{E} \]
Plugging in the given energy to remove an electron from an iron atom (\( 7.21 \times 10^{-19} \) J), and the values of \( h \) and \( c \), we can calculate the maximum wavelength.
\[ \lambda = \frac{(6.626 \times 10^{-34} \mathrm{~J \cdot s})(3.00 \times 10^8 \mathrm{~m/s})}{7.21 \times 10^{-19} \mathrm{~J}} \]
\[ \lambda \approx \frac{(1.99 \times 10^{-25} \mathrm{~J \cdot m})}{7.21 \times 10^{-19} \mathrm{~J}} \]
\[ \lambda \approx 2.76 \times 10^{-7} \mathrm{~m} \]
So, the maximum wavelength of light that can remove an electron from an iron atom is approximately \( 2.76 \times 10^{-7} \) meters.
