A proton has kinetic energy $$E = 100\,keV$$ which is equal to that of a photon. The wavelength of photon is $${\lambda _2}$$ and that of proton is $${\lambda _1}.$$ The ration of $$\frac{{{\lambda _2}}}{{{\lambda _1}}}$$ is proportional to

Question

A proton has kinetic energy $$E = 100\,keV$$ which is equal to that of a photon. The wavelength of photon is $${\lambda _2}$$ and that of proton is $${\lambda _1}.$$ The ration of $$\frac{{{\lambda _2}}}{{{\lambda _1}}}$$ is proportional to

A. $${E^2}$$

B. $${E^{\frac{1}{2}}}$$

C. $${E^{ - 1}}$$

D. $${E^{ - \frac{1}{2}}}$$

Answer : $${E^{ - \frac{1}{2}}}$$

Solution :
For photon,
$${\lambda _2} = \frac{{hc}}{E}\,......\left( {\text{i}} \right)$$
For proton, $$p = \sqrt {2mE} $$
$$\eqalign{ & {\lambda _1} = \frac{h}{p} = \frac{h}{{\sqrt {2mE} }}\,......\left( {{\text{ii}}} \right) \cr & \frac{{{\lambda _2}}}{{{\lambda _1}}} = \frac{{hc}}{{E \times \frac{h}{{\sqrt {2mE} }}}} \propto {E^{ - \frac{1}{2}}} \cr} $$

Releted MCQ Question on
Modern Physics >> Dual Nature of Matter and Radiation

Releted Question 1

A particle of mass $$M$$ at rest decays into two particles of masses $${m_1}$$ and $${m_2},$$ having non-zero velocities. The ratio of the de Broglie wavelengths of the particles, $$\frac{{{\lambda _1}}}{{{\lambda _2}}},$$ is

A. $$\frac{{{m_1}}}{{{m_2}}}$$

B. $$\frac{{{m_2}}}{{{m_1}}}$$

C. 1.0

D. $$\frac{{\sqrt {{m_2}} }}{{\sqrt {{m_1}} }}$$

Releted Question 2

A proton has kinetic energy $$E = 100\,keV$$ which is equal to that of a photon. The wavelength of photon is $${\lambda _2}$$ and that of proton is $${\lambda _1}.$$ The ration of $$\frac{{{\lambda _2}}}{{{\lambda _1}}}$$ is proportional to

A. $${E^2}$$

B. $${E^{\frac{1}{2}}}$$

C. $${E^{ - 1}}$$

D. $${E^{ - \frac{1}{2}}}$$

Releted Question 3

A beam of electron is used in an YDSE experiment. The slit width is $$d.$$ When the velocity of electron is increased, then

A. no interference is observed

B. fringe width increases

C. fringe width decreases

D. fringe width remains same

Releted Question 4

Formation of covalent bonds in compounds exhibits

A. wave nature of electron

B. particle nature of electron

C. both wave and particle nature of electron

D. none of these

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Dual Nature of Matter and Radiation

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