Threshold Wavelength And Work Function

Question

A clean metal surface used in a photocell has a work function of $2.0\ 	ext{eV}$ for electron emission. Beyond which longest wavelength of incident light will the surface fail to emit photoelectrons?

RankGuru · Accepted Answer

Photoelectric emission occurs only when each photon carries at least the work function $\phi_0$, the minimum energy needed to liberate an electron from the metal surface. The threshold (longest) wavelength $\lambda_0$ corresponds to a photon energy exactly equal to $\phi_0$, so $\phi_0=\dfrac{hc}{\lambda_0}$. Using the convenient product $hc=1240\ 	ext{eV nm}$, we get $\lambda_0=\dfrac{1240}{2.0}=620\ 	ext{nm}$. Light of longer wavelength has lower photon energy and cannot eject any electron, no matter how intense it is. The option $310\ 	ext{nm}$ wrongly doubles the work function. The option $1240\ 	ext{nm}$ takes the work function as $1\ 	ext{eV}$. The option $413\ 	ext{nm}$ corresponds to $3\ 	ext{eV}$. This threshold concept is central to the NCERT treatment of Hertz's and Lenard's observations and to Einstein's photoelectric equation. A sanity check: $620\ 	ext{nm}$ lies in the orange-red region, so only photons bluer than this can release electrons, consistent with a modest $2.0\ 	ext{eV}$ barrier.

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Threshold Wavelength And Work Function

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...

Inside a reactor a neutron of mass 1.67×10−27 kg has been slowed to thermal equili...

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 ...