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Chapter 17: Problem 2416

Calculate the energy of a photon of radian wavelength \(6000 \AA\) in \(\mathrm{eV}\) (A) \(20.6 \mathrm{eV}\) (B) \(2.06 \mathrm{eV}\) (C) \(1.03 \mathrm{eV}\) (D) \(4.12 \mathrm{eV}\)

Short Answer

Expert verified
The energy of a photon with a wavelength of \(6000 \mathrm{\AA}\) is approximately \(2.07 \mathrm{eV}\), which is closest to option (B), \(2.06 \mathrm{eV}\).

Step by step solution

01

Write down the formula for the energy of a photon

The formula for the energy of a photon is given by: \(E = \dfrac{hc}{\lambda}\), where \(E\) is the energy of the photon, \(h\) is Planck's constant (approximated to \(6.63 \times 10^{-34} \mathrm{J·s}\)), \(c\) is the speed of light (approximated to \(3 \times 10^8 \mathrm{m/s}\)), and \(\lambda\) is the wavelength of the photon.
02

Convert the given wavelength from angstroms to meters

The wavelength is given as \(6000 \mathrm{\AA}\) (angstroms). To convert this to meters, we can use the conversion factor \(1 \mathrm{\AA} = 10^{-10} \mathrm{m}\). \(\lambda = 6000 \mathrm{\AA} \times \dfrac{10^{-10} \mathrm{m}}{1 \mathrm{\AA}} = 6000 \times 10^{-10} \mathrm{m}\)
03

Calculate the energy of the photon in joules

Using the formula from Step 1 and the wavelength in meters, we can calculate the energy of the photon in joules: \(E = \dfrac{(6.63 × 10^{-34} \mathrm{J·s}) \times (3 × 10^8 \mathrm{m/s})}{(6000 × 10^{-10} \mathrm{m})}\) \(E = \dfrac{1.989 × 10^{-25} \mathrm{J·m}}{6 × 10^{-7} \mathrm{m}}\) \(E = 3.315 × 10^{-19} \mathrm{J}\)
04

Convert energy from joules to electron volts

To convert the energy from joules to electron volts, we can use the conversion factor \(1 \mathrm{eV} = 1.602 \times 10^{-19} \mathrm{J}\): \(E_\mathrm{eV} = \dfrac{3.315 \times 10^{-19} \mathrm{J}}{1.602 \times 10^{-19} \mathrm{J/eV}}\) \(E_\mathrm{eV} \approx 2.07 \mathrm{eV}\)
05

Determine the correct answer from the options given

Based on our calculations, the correct answer is approximately \(2.07 \mathrm{eV}\) which is closest to option (B). So the correct answer is: (B) \(2.06 \mathrm{eV}\)

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Most popular questions from this chapter

Work function of metal is \(2.5 \mathrm{eV}\) If wave length of light incident on metal plate is \(3000 \AA\), stopping potential of emitted electron will be....... $\left\\{\mathrm{h}=6.62 \times 10^{-34} \mathrm{~J} . \mathrm{s}, \mathrm{c}=3 \times 10^{8}(\mathrm{~m} / \mathrm{s})\right\\}$ (A) \(0.82 \mathrm{~V}\) (B) \(0.41 \mathrm{~V}\) (C) \(1.64 \mathrm{~V}\) (D) \(3.28 \mathrm{~V}\)

According to Einstein's photoelectric equation, graph of kinetic energy of emitted photo electrons from metal versus frequency of incident radiation is linear. Its slope.......... (A) depends on type of metal used (B) depends on intensity of radiation (C) depends on both metal used and intensity of radiation. (D) is same for all metals and free from intensity of radiation.

An image of sun is formed by a lens of focal length \(30 \mathrm{~cm}\) on the metal surface of a photo-electric cell and a photoelectric current (I) is produced. The lens forming the image is then replaced by another of the same diameter but of focal length of \(15 \mathrm{~cm}\). The photoelectric current in this case is \(\ldots \ldots \ldots\) (A) \((1 / 2)\) (B) 1 (C) \(2 \mathrm{I}\) (D) \(4 \mathrm{I}\)

de-Broglie wavelength of atom at T \(\mathrm{K}\) absolute temperature will be \(\ldots \ldots \ldots\) (A) \([\mathrm{h} /\\{\mathrm{mkT}\\}]\) (B) \([\mathrm{h} /\\{\sqrt{3} \mathrm{mKT}\\}]\) (C) \([\\{\sqrt{2} \mathrm{mKT}\\} / \mathrm{h}]\) (D) \(\sqrt{(2 \mathrm{mKT})}\)

Direction Read the following question choose if: (a) Both Assertion and Reason are true and Reason is correct explanation of Assertion. (b) Both Assertion and Reason are true, but Reason is not correct explanation of Assertion. (c) Assertion is true but the Reason is false. (d) Both Assertion and Reason is false. Assertion: Metals like Na or \(\mathrm{K}\), emit electrons even when visible lights fall on them. Reason: This is because their work function is low. (A) a (B) \(\mathrm{b}\) (C) \(\mathrm{c}\) (D) d
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