357579
If \(m\) is the mass of an electron and \(c\) is the speed of light the ratio of the wavelengths of photon of energy \(E\) to that of the electron of the same energy:
1 \(c \sqrt{\dfrac{2 m}{E}}\)
2 \(\sqrt{\dfrac{2 m}{E}}\)
3 \(\sqrt{\dfrac{2 m}{c E}}\)
4 \(\sqrt{\dfrac{m}{E}}\)
Explanation:
Energy of photon \(E=h v=\dfrac{h c}{\lambda_{p}}\) \(\lambda_{p}=\dfrac{h c}{E}\) Wavelength of electron \(\lambda_{e}=\dfrac{h}{\sqrt{2 m E}}\) \(\therefore \dfrac{\lambda_{p}}{\lambda_{e}}=\dfrac{h c}{E} \times \dfrac{\sqrt{2 m E}}{h}=c \sqrt{\dfrac{2 m}{E}} \text {. }\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER
357580
Assertion : A photon has no rest mass, yet it carries definite momentum. Reason : Momentum of photon is due to its energy and hence its equivalent mass.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
\(m_{0}=0\) for photon. But \(m=\dfrac{h}{\lambda v}\) We also know \(p=m v\) \(E=h v=\dfrac{h c}{\lambda}\) \(\Rightarrow p=\dfrac{E}{c}\) So correct option is (1).
PHXII11:DUAL NATURE OF RADIATION AND MATTER
357581
\(n\) ' photons of wavelength ' \(\lambda\) ' are absorbed by a black body of mass ' \(m\) '. The momentum gained by the body is
1 \(\frac{h}{{m\lambda }}\)
2 \(\frac{{mnh}}{\lambda }\)
3 \(\frac{{nh}}{{m\lambda }}\)
4 \(\frac{{nh}}{\lambda }\)
Explanation:
Energy of \(n\) protons, \(E = \frac{{nhc}}{\lambda }\) Momentum gained by the body, \(p = \frac{E}{c}\) \( = \frac{{nhc}}{{\lambda c}} = \frac{{nh}}{\lambda }\)
KCET - 2012
PHXII11:DUAL NATURE OF RADIATION AND MATTER
357582
Assertion : An electron microscope is based on de Broglie hypothesis. Reason : A beam of electrons behaves as a wave which can be converged by electric and magnetic lenses.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Electron microscopes, based on in de Broglie's wavelength concept, utilize short electron wavelengths for high-resolution imaging. Their superiority over optical microscopes lies in the ability to resolve atomic and molecular details. So correct option is (1).
NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXII11:DUAL NATURE OF RADIATION AND MATTER
357579
If \(m\) is the mass of an electron and \(c\) is the speed of light the ratio of the wavelengths of photon of energy \(E\) to that of the electron of the same energy:
1 \(c \sqrt{\dfrac{2 m}{E}}\)
2 \(\sqrt{\dfrac{2 m}{E}}\)
3 \(\sqrt{\dfrac{2 m}{c E}}\)
4 \(\sqrt{\dfrac{m}{E}}\)
Explanation:
Energy of photon \(E=h v=\dfrac{h c}{\lambda_{p}}\) \(\lambda_{p}=\dfrac{h c}{E}\) Wavelength of electron \(\lambda_{e}=\dfrac{h}{\sqrt{2 m E}}\) \(\therefore \dfrac{\lambda_{p}}{\lambda_{e}}=\dfrac{h c}{E} \times \dfrac{\sqrt{2 m E}}{h}=c \sqrt{\dfrac{2 m}{E}} \text {. }\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER
357580
Assertion : A photon has no rest mass, yet it carries definite momentum. Reason : Momentum of photon is due to its energy and hence its equivalent mass.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
\(m_{0}=0\) for photon. But \(m=\dfrac{h}{\lambda v}\) We also know \(p=m v\) \(E=h v=\dfrac{h c}{\lambda}\) \(\Rightarrow p=\dfrac{E}{c}\) So correct option is (1).
PHXII11:DUAL NATURE OF RADIATION AND MATTER
357581
\(n\) ' photons of wavelength ' \(\lambda\) ' are absorbed by a black body of mass ' \(m\) '. The momentum gained by the body is
1 \(\frac{h}{{m\lambda }}\)
2 \(\frac{{mnh}}{\lambda }\)
3 \(\frac{{nh}}{{m\lambda }}\)
4 \(\frac{{nh}}{\lambda }\)
Explanation:
Energy of \(n\) protons, \(E = \frac{{nhc}}{\lambda }\) Momentum gained by the body, \(p = \frac{E}{c}\) \( = \frac{{nhc}}{{\lambda c}} = \frac{{nh}}{\lambda }\)
KCET - 2012
PHXII11:DUAL NATURE OF RADIATION AND MATTER
357582
Assertion : An electron microscope is based on de Broglie hypothesis. Reason : A beam of electrons behaves as a wave which can be converged by electric and magnetic lenses.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Electron microscopes, based on in de Broglie's wavelength concept, utilize short electron wavelengths for high-resolution imaging. Their superiority over optical microscopes lies in the ability to resolve atomic and molecular details. So correct option is (1).
357579
If \(m\) is the mass of an electron and \(c\) is the speed of light the ratio of the wavelengths of photon of energy \(E\) to that of the electron of the same energy:
1 \(c \sqrt{\dfrac{2 m}{E}}\)
2 \(\sqrt{\dfrac{2 m}{E}}\)
3 \(\sqrt{\dfrac{2 m}{c E}}\)
4 \(\sqrt{\dfrac{m}{E}}\)
Explanation:
Energy of photon \(E=h v=\dfrac{h c}{\lambda_{p}}\) \(\lambda_{p}=\dfrac{h c}{E}\) Wavelength of electron \(\lambda_{e}=\dfrac{h}{\sqrt{2 m E}}\) \(\therefore \dfrac{\lambda_{p}}{\lambda_{e}}=\dfrac{h c}{E} \times \dfrac{\sqrt{2 m E}}{h}=c \sqrt{\dfrac{2 m}{E}} \text {. }\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER
357580
Assertion : A photon has no rest mass, yet it carries definite momentum. Reason : Momentum of photon is due to its energy and hence its equivalent mass.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
\(m_{0}=0\) for photon. But \(m=\dfrac{h}{\lambda v}\) We also know \(p=m v\) \(E=h v=\dfrac{h c}{\lambda}\) \(\Rightarrow p=\dfrac{E}{c}\) So correct option is (1).
PHXII11:DUAL NATURE OF RADIATION AND MATTER
357581
\(n\) ' photons of wavelength ' \(\lambda\) ' are absorbed by a black body of mass ' \(m\) '. The momentum gained by the body is
1 \(\frac{h}{{m\lambda }}\)
2 \(\frac{{mnh}}{\lambda }\)
3 \(\frac{{nh}}{{m\lambda }}\)
4 \(\frac{{nh}}{\lambda }\)
Explanation:
Energy of \(n\) protons, \(E = \frac{{nhc}}{\lambda }\) Momentum gained by the body, \(p = \frac{E}{c}\) \( = \frac{{nhc}}{{\lambda c}} = \frac{{nh}}{\lambda }\)
KCET - 2012
PHXII11:DUAL NATURE OF RADIATION AND MATTER
357582
Assertion : An electron microscope is based on de Broglie hypothesis. Reason : A beam of electrons behaves as a wave which can be converged by electric and magnetic lenses.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Electron microscopes, based on in de Broglie's wavelength concept, utilize short electron wavelengths for high-resolution imaging. Their superiority over optical microscopes lies in the ability to resolve atomic and molecular details. So correct option is (1).
357579
If \(m\) is the mass of an electron and \(c\) is the speed of light the ratio of the wavelengths of photon of energy \(E\) to that of the electron of the same energy:
1 \(c \sqrt{\dfrac{2 m}{E}}\)
2 \(\sqrt{\dfrac{2 m}{E}}\)
3 \(\sqrt{\dfrac{2 m}{c E}}\)
4 \(\sqrt{\dfrac{m}{E}}\)
Explanation:
Energy of photon \(E=h v=\dfrac{h c}{\lambda_{p}}\) \(\lambda_{p}=\dfrac{h c}{E}\) Wavelength of electron \(\lambda_{e}=\dfrac{h}{\sqrt{2 m E}}\) \(\therefore \dfrac{\lambda_{p}}{\lambda_{e}}=\dfrac{h c}{E} \times \dfrac{\sqrt{2 m E}}{h}=c \sqrt{\dfrac{2 m}{E}} \text {. }\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER
357580
Assertion : A photon has no rest mass, yet it carries definite momentum. Reason : Momentum of photon is due to its energy and hence its equivalent mass.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
\(m_{0}=0\) for photon. But \(m=\dfrac{h}{\lambda v}\) We also know \(p=m v\) \(E=h v=\dfrac{h c}{\lambda}\) \(\Rightarrow p=\dfrac{E}{c}\) So correct option is (1).
PHXII11:DUAL NATURE OF RADIATION AND MATTER
357581
\(n\) ' photons of wavelength ' \(\lambda\) ' are absorbed by a black body of mass ' \(m\) '. The momentum gained by the body is
1 \(\frac{h}{{m\lambda }}\)
2 \(\frac{{mnh}}{\lambda }\)
3 \(\frac{{nh}}{{m\lambda }}\)
4 \(\frac{{nh}}{\lambda }\)
Explanation:
Energy of \(n\) protons, \(E = \frac{{nhc}}{\lambda }\) Momentum gained by the body, \(p = \frac{E}{c}\) \( = \frac{{nhc}}{{\lambda c}} = \frac{{nh}}{\lambda }\)
KCET - 2012
PHXII11:DUAL NATURE OF RADIATION AND MATTER
357582
Assertion : An electron microscope is based on de Broglie hypothesis. Reason : A beam of electrons behaves as a wave which can be converged by electric and magnetic lenses.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Electron microscopes, based on in de Broglie's wavelength concept, utilize short electron wavelengths for high-resolution imaging. Their superiority over optical microscopes lies in the ability to resolve atomic and molecular details. So correct option is (1).