Question

The ratio of the energy of photon \(2000 A\) wavelength radiation to that of \(4000 A\) radiation is (1) \(1 / 4\) (2) \(1 / 2\) (3) 2 (4) 4

Short answer

The ratio of the energy of 2000 Å radiation to that of 4000 Å radiation is 2.

Step-by-step solution

- Understanding Photon Energy

Photon energy is given by the formula \( E = \frac {hc}{\lambda} \), where \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength of the photon.

- Calculate Energy for 2000 Å Radiation

Substitute \( \lambda = 2000 Å = 2000 \times 10^{-10} \) meters into the energy formula: \( E_1 = \frac {hc}{2000 \times 10^{-10}} \)

- Calculate Energy for 4000 Å Radiation

Substitute \( \lambda = 4000 Å = 4000 \times 10^{-10}\) meters into the energy formula: \( E_2 = \frac {hc}{4000 \times 10^{-10}} \)

- Ratio of Energies

Divide the energy of 2000 Å radiation by the energy of 4000 Å radiation: \( \frac{E_1}{E_2} = \frac{\frac{hc}{2000 \times 10^{-10}}}{\frac{hc}{4000 \times 10^{-10}}} = \frac{4000 \times 10^{-10}}{2000 \times 10^{-10}} = 2 \)

Key concepts

Photon Energy Formula

To understand the energy of a photon, we need to use a specific formula. The formula is:
\( E = \frac{hc}{\lambda} \). Here,

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