Energy Of A Photon

Question

A sodium vapour lamp emits monochromatic light whose frequency is measured to be $6	imes10^{14}\ 	ext{Hz}$. What is the energy carried by a single photon of this radiation?

RankGuru · Accepted Answer

According to Planck's quantum hypothesis, electromagnetic radiation of frequency $
u$ is emitted and absorbed in discrete packets called photons, each carrying energy $E=h
u$, where $h=6.6	imes10^{-34}\ 	ext{J s}$ is Planck's constant. The energy depends only on the frequency of the light and is completely independent of the intensity, which merely fixes how many photons are present. Substituting the given frequency, $E=6.6	imes10^{-34}	imes6	imes10^{14}=3.96	imes10^{-19}\ 	ext{J}$, which equals about $2.48\ 	ext{eV}$. The value $2.64	imes10^{-19}\ 	ext{J}$ is wrong because it corresponds to a lower frequency of $4	imes10^{14}\ 	ext{Hz}$. The value $1.98	imes10^{-19}\ 	ext{J}$ wrongly uses half the stated frequency. The value $5.28	imes10^{-19}\ 	ext{J}$ overestimates the frequency as $8	imes10^{14}\ 	ext{Hz}$. This is the same photon relation introduced in the NCERT chapter on dual nature, underpinning Einstein's explanation of the photoelectric effect. A quick check confirms the answer lies in the visible-light range of a few electron-volts, which is physically reasonable for yellow sodium light.

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Energy Of A Photon

Select the correct option:

🔒 Solution Hidden from View

More dual nature of radiation and matter Practice Questions

In a landmark experiment a beam of low-energy electrons was scattered from a single nickel crystal a...

A metal surface of work function 1.0 eV is illuminated separately by light of wavelength $...

In a photoelectric experiment the stopping potential rises from 0.50 V to 2.15 V...

An electron and a proton are observed to have exactly the same de Broglie wavelength as they move th...

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Identical electrons are accelerated from rest, one through a potential difference of 50 V ...

Keeping the frequency of incident light fixed above threshold, an experimenter gradually doubles the...

Green light of wavelength 5×10−7 m from a laser pointer is incident normally on a ...

During a photoelectric experiment the reverse voltage at which the photocurrent just becomes zero is...

Ultraviolet light of wavelength 400 nm illuminates a metal whose work function is $2.0\ \t...

Monochromatic radiation of wavelength 248 nm falls on a photosensitive cathode whose work ...

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About This Question

Solution

A metal surface of work function $1.0 eV$ is illuminated separately by light of wavelength $...

In a photoelectric experiment the stopping potential rises from $0.50 V$ to $2.15 V$ ...

Inside a reactor a neutron of mass $1.67 \times 1 0^{- 27} kg$ has been slowed to thermal equili...

Identical electrons are accelerated from rest, one through a potential difference of $50 V$ ...

Green light of wavelength $5 \times 1 0^{- 7} m$ from a laser pointer is incident normally on a ...

Ultraviolet light of wavelength $400 nm$ illuminates a metal whose work function is $2.0\ \t...

Monochromatic radiation of wavelength $248 nm$ falls on a photosensitive cathode whose work ...