Questions: An X-ray has a wavelength of 1.87 Å. Calculate the energy (in J) of one photon of this radiation. (10^10 Å=1 m). Round your answer to 3 significant figures.

Solution Steps

First, we need to convert the given wavelength from angstroms (\(\AA\)) to meters (m). The given wavelength is \(1.87 \AA\).

\[ 1 \AA = 10^{-10} \text{ m} \]

\[ 1.87 \AA = 1.87 \times 10^{-10} \text{ m} \]

The energy \(E\) of a photon is related to its wavelength \(\lambda\) by the equation:

\[ E = \frac{hc}{\lambda} \]

where:

• \(h\) is Planck's constant (\(6.6261 \times 10^{-34} \text{ J} \cdot \text{s}\))
• \(c\) is the speed of light (\(2.998 \times 10^8 \text{ m/s}\))
• \(\lambda\) is the wavelength in meters

Substitute the values into the equation:

\[ E = \frac{(6.6261 \times 10^{-34} \text{ J} \cdot \text{s}) \times (2.998 \times 10^8 \text{ m/s})}{1.87 \times 10^{-10} \text{ m}} \]

\[ E = \frac{1.9862 \times 10^{-25} \text{ J} \cdot \text{m}}{1.87 \times 10^{-10} \text{ m}} \]

\[ E = 1.0624 \times 10^{-15} \text{ J} \]

Finally, we round the result to 3 significant figures:

\[ E \approx 1.06 \times 10^{-15} \text{ J} \]

Final Answer