Chapter 22, Problem 47QAP

To determine

(a)

The wavelength and frequency of photon that have the energy $2.33\times {10}^{-19}J$ ?

Explanation of Solution

Calculation:

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{2.33\times {10}^{-19}}=8.57\times {10}^{-7}m=857nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{2.33\times {10}^{-19}}{6.63\times {10}^{-34}}=3.51\times {10}^{14}Hz$

Conclusion:

Wavelength $=857nm$

Frequency $=3.51\times {10}^{14}Hz$

To determine

(b)

The wavelength and frequency of photon that have the energy $4.50\times {10}^{-19}J$ ?

Explanation of Solution

Calculation:

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{4.5\times {10}^{-19}}=4.42\times {10}^{-7}m=442nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{4.50\times {10}^{-19}}{6.63\times {10}^{-34}}=6.79\times {10}^{14}Hz$

Conclusion:

Wavelength $=442nm$

Frequency $=6.79\times {10}^{14}Hz$

To determine

(c)

The wavelength and frequency of photon that have the energy $3.20\times {10}^{-19}J$ ?

Explanation of Solution

Calculation:

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{3.20\times {10}^{-19}}=6.22\times {10}^{-7}m=622nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{3.20\times {10}^{-19}}{6.63\times {10}^{-34}}=4.83\times {10}^{14}Hz$

Conclusion:

Wavelength $=622nm$

Frequency $=4.83\times {10}^{14}Hz$

To determine

(d)

The wavelength and frequency of photon that have the energy $8.55\times {10}^{-19}J$ ?

Explanation of Solution

Calculation:

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{8.55\times {10}^{-19}}=2.33\times {10}^{-7}m=233nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{8.55\times {10}^{-19}}{6.63\times {10}^{-34}}=1.29\times {10}^{15}Hz$

Conclusion:

Wavelength $=233nm$

Frequency $=1.29\times {10}^{15}Hz$

To determine

(e)

The wavelength and frequency of photon that have the energy $63.3eV$ ?

Explanation of Solution

Calculation:

Energy in joules,
  $E_{photon}=63.3\times 1.60\times {10}^{-19}=1.01\times {10}^{-17}J$

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{1.01\times {10}^{-17}}=1.96\times {10}^{-8}m=19.6nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{1.01\times {10}^{-17}}{6.63\times {10}^{-34}}=1.53\times {10}^{16}Hz$

Conclusion:

Wavelength $=19.6nm$

Frequency $=1.53\times {10}^{16}Hz$

To determine

(f)

The wavelength and frequency of photon that have the energy $8.77eV$ ?

Explanation of Solution

Calculation:

Energy in joules,
  $E_{photon}=8.77\times 1.60\times {10}^{-19}=1.40\times {10}^{-18}J$

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{1.40\times {10}^{-18}}=1.42\times {10}^{-8}m=14.2nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{1.40\times {10}^{-18}}{6.63\times {10}^{-34}}=2.12\times {10}^{15}Hz$

Conclusion:

Wavelength $=14.2nm$

Frequency $=2.12\times {10}^{15}Hz$

To determine

(g)

The wavelength and frequency of photon that have the energy $1.98eV$ ?

Explanation of Solution

Calculation:

Energy in joules,
  $E_{photon}=1.98\times 1.60\times {10}^{-19}=3.17\times {10}^{-19}J$

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{3.17\times {10}^{-19}}=6.28\times {10}^{-7}m=628nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{3.17\times {10}^{-19}}{6.63\times {10}^{-34}}=4.78\times {10}^{14}Hz$

Conclusion:

Wavelength $=628nm$

Frequency $=4.78\times {10}^{14}Hz$

To determine

(h)

The wavelength and frequency of photon that have the energy $4.55eV$ ?

Explanation of Solution

Calculation:

Energy in joules,
  $E_{photon}=4.55\times 1.60\times {10}^{-19}=7.28\times {10}^{-19}J$

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{7.28\times {10}^{-19}}=2.73\times {10}^{-7}m=273nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{7.28\times {10}^{-19}}{6.63\times {10}^{-34}}=1.10\times {10}^{15}Hz$

Conclusion:

Wavelength $=273nm$

Frequency $=1.10\times {10}^{15}Hz$