Chapter 22, Problem 48QAP

To determine

(a)

The wavelength and frequency of photon that have the energy $3.45\times {10}^{-19}J$ ?

Explanation of Solution

Given info:

Formula used:

Calculation:

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{3.45\times {10}^{-19}}=5.77\times {10}^{-7}m=577nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{3.45\times {10}^{-19}}{6.63\times {10}^{-34}}=5.20\times {10}^{14}Hz$

Conclusion:

Wavelength $=577nm$

Frequency $=5.20\times {10}^{14}Hz$

To determine

(b)

The wavelength and frequency of photon that have the energy $4.80\times {10}^{-19}J$ ?

Explanation of Solution

Calculation:

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{4.8\times {10}^{-19}}=4.14\times {10}^{-7}m=414nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{4.80\times {10}^{-19}}{6.63\times {10}^{-34}}=7.24\times {10}^{14}Hz$

Conclusion:

Wavelength $=414nm$

Frequency $=7.24\times {10}^{14}Hz$

To determine

(a)

The wavelength and frequency of photon that have the energy $1.28\times {10}^{-18}J$ ?

Explanation of Solution

Calculation:

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{1.28\times {10}^{-18}}=1.55\times {10}^{-7}m=155nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{1.28\times {10}^{-18}}{6.63\times {10}^{-34}}=1.93\times {10}^{15}Hz$

Conclusion:

Wavelength $=155nm$

Frequency $=1.93\times {10}^{15}Hz$

To determine

(a)

The wavelength and frequency of photon that have the energy $4.33\times {10}^{-20}J$ ?

Explanation of Solution

Calculation:

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{4.33\times {10}^{-20}}=4.59\times {10}^{-7}m=459nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{4.33\times {10}^{-20}}{6.63\times {10}^{-34}}=6.53\times {10}^{13}Hz$

Conclusion:

Wavelength $=459nm$

Frequency $=6.53\times {10}^{13}Hz$

To determine

(e)

The wavelength and frequency of photon that have the energy $931MeV$ ?

Explanation of Solution

Calculation:

Energy in joules,
  $E_{photon}=931\times {10}^6\times 1.60\times {10}^{-19}=1.49\times {10}^{-10}J$

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{1.49\times {10}^{-10}}=1.34\times {10}^{-15}m$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{1.49\times {10}^{-10}}{6.63\times {10}^{-34}}=2.25\times {10}^{23}Hz$

Conclusion:

Wavelength $=1.34\times {10}^{-15}m$

Frequency $=2.25\times {10}^{23}Hz$

To determine

(f)

The wavelength and frequency of photon that have the energy $2.88keV$ ?

Explanation of Solution

Calculation:

Energy in joules,
  $E_{photon}=2.88\times {10}^3\times 1.60\times {10}^{-19}=4.61\times {10}^{-16}J$

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{4.61\times {10}^{-16}}=4.32\times {10}^{-10}m=0.432nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{4.61\times {10}^{-16}}{6.63\times {10}^{-34}}=6.95\times {10}^{17}Hz$

Conclusion:

Wavelength $=0.432nm$

Frequency $=6.95\times {10}^{17}Hz$

To determine

(g)

The wavelength and frequency of photon that have the energy $7.88eV$ ?

Explanation of Solution

Calculation:

Energy in joules,
  $E_{photon}=7.88\times 1.60\times {10}^{-19}=1.26\times {10}^{-18}J$

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{1.26\times {10}^{-18}}=1.58\times {10}^{-7}m=158nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{1.26\times {10}^{-18}}{6.63\times {10}^{-34}}=1.90\times {10}^{15}Hz$

Conclusion:

Wavelength $=158nm$

Frequency $=1.90\times {10}^{15}Hz$

To determine

(h)

The wavelength and frequency of photon that have the energy $13.6eV$ ?

Explanation of Solution

Calculation:

Energy in joules,
  $E_{photon}=13.6\times 1.60\times {10}^{-19}=2.18\times {10}^{-18}J$

Wavelength
  $\lambda =\frac{hc}{E_{photon}}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{2.18\times {10}^{-18}}=9.14\times {10}^{-8}m=91.4nm$

Frequency
  $f=\frac{E_{photon}}{h}=\frac{2.18\times {10}^{-18}}{6.63\times {10}^{-34}}=3.28\times {10}^{15}Hz$

Conclusion:

Wavelength $=91.4nm$

Frequency $=3.28\times {10}^{15}Hz$