Question

Find out voltage applied to an electron microscope to produce electron of wavelength 0.6A.​

Answer 1

your answer

Electrons are accelerated by a voltage, V= 50 kV =image452 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

Charge on an electron, e=image453 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

Mass of an electron, me=image454 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

Wavelength of yellow light = image455 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

The kinetic energy of the electron is given as:

E= eV

image456 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

image457 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

De Broglie wavelength is given by the relation:

image458 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

image459 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2image460 NCERT Solutions class-12 physics Dual Nature of Radiation and Matter Part-2

This wavelength is nearly 105 times less than the wavelength of yellow light.

The resolving power of a microscope is inversely proportional to the wavelength of light used. Thus, the resolving power of an electron microscope is nearly 105times that of an optical microscope.

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Answer 2

The voltage applied to an electron is 4.52 volts

Explanation:

Given that,

Wavelength of the electron, $\lambda=0.6\ A=0.6\times 10^{-10}\ m$

The relation between voltage and the wavelength is given by :

$\lambda=\dfrac{h}{\sqrt{2meV}}$

$\lambda=\dfrac{1.227}{\sqrt{V} }\times 10^{-9}\ m$

$\sqrt{V}=\dfrac{1.227}{\lambda}\times 10^{-9}\ m$

$\sqrt{V}=\dfrac{1.227}{0.6\times 10^{-10}}\times 10^{-9}\ m$

V = 4.52 volts

So, the voltage applied to an electron is 4.52 volts. Hence, this is the required solution.

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Topic : De- Broglie wavelength

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