Question

For an orbit radius of \[5.3\times10^{-11}\,\mathrm{m}\] and an electron velocity of \[2.2\times10^6\,\mathrm{m\,s^{-1}}\], what is the approximate initial frequency of emitted light according to classical electromagnetic theory?

Options

• \[5.3\times10^{-11}\,\mathrm{Hz}\]

• \[6.6\times10^{15}\,\mathrm{Hz}\]

• \[2.2\times10^6\,\mathrm{Hz}\]

• \[6.6\times10^{11}\,\mathrm{Hz}\]

Answer 1

\[ r = 5.3 \times 10^{-11}\ \mathrm{m}, \qquad v = 2.2 \times 10^{6}\ \mathrm{m\,s^{-1}} \]

\[ \nu = \dfrac{v}{2\pi r} \]

\[ 2\pi r = 2 \times 3.14 \times 5.3 \times 10^{-11} = 3.33 \times 10^{-10}\ \mathrm{m} \]

\[ \nu = \dfrac{2.2 \times 10^{6}}{3.33 \times 10^{-10}} \]

\[ \nu = 0.66 \times 10^{6 \,+\, 10} = 0.66 \times 10^{16}\ \mathrm{Hz} \]

\[ \therefore \quad \nu \approx 6.6 \times 10^{15}\ \mathrm{Hz} \]