Wave Nature of Matter
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357871 The potential energy of a particle of mass \(m\) is given by
\(U(x)= \begin{cases}E_{0}: & 0 \leq x \leq 1 \\ 0 ; & x>1\end{cases}\)
\(\lambda_{1}\) and \(\lambda_{2}\) are the de Broglie wavelength of the particle, when \(0 \leq x \leq 1\) and \(x>1\) respectively. If the total energy of particle is \(2 E_{0}\), the ratio \(\dfrac{\lambda_{1}}{\lambda_{2}}\) will be

1 1
2 2
3 \(\dfrac{1}{\sqrt{2}}\)
4 \(\sqrt{2}\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357872 A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is
(Assume \(h = 6.63 \times {10^{ - 34}}Js,\) \({m_e} = 9.0 \times {10^{ - 31}}\;kg\) and \({m_p} = 1836\,\,{\text{times}}\,\,{m_e})\)

1 1:1836
2 \(1: \dfrac{1}{1836}\)
3 \(1: \sqrt{1836}\)
4 \(1: \dfrac{1}{\sqrt{1836}}\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357873 Choose the correct statement

1 Any charged particle in rest is accompanied by matter waves.
2 Any uncharged particle in rest is accompanied by matter waves.
3 The matter waves are waves of zero amplitude.
4 The matter waves are waves of probability amplitude.
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357874 The de Broglie wavelength associated with a particle of mass \(m\), moving with a velocity \(v\) and energy \(E\) is given by

1 \(h / m v^{2}\)
2 \(m v / h^{2}\)
3 \(h / \sqrt{2 m E}\)
4 \(\sqrt{2 m E} / h^{2}\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357871 The potential energy of a particle of mass \(m\) is given by
\(U(x)= \begin{cases}E_{0}: & 0 \leq x \leq 1 \\ 0 ; & x>1\end{cases}\)
\(\lambda_{1}\) and \(\lambda_{2}\) are the de Broglie wavelength of the particle, when \(0 \leq x \leq 1\) and \(x>1\) respectively. If the total energy of particle is \(2 E_{0}\), the ratio \(\dfrac{\lambda_{1}}{\lambda_{2}}\) will be

1 1
2 2
3 \(\dfrac{1}{\sqrt{2}}\)
4 \(\sqrt{2}\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357872 A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is
(Assume \(h = 6.63 \times {10^{ - 34}}Js,\) \({m_e} = 9.0 \times {10^{ - 31}}\;kg\) and \({m_p} = 1836\,\,{\text{times}}\,\,{m_e})\)

1 1:1836
2 \(1: \dfrac{1}{1836}\)
3 \(1: \sqrt{1836}\)
4 \(1: \dfrac{1}{\sqrt{1836}}\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357873 Choose the correct statement

1 Any charged particle in rest is accompanied by matter waves.
2 Any uncharged particle in rest is accompanied by matter waves.
3 The matter waves are waves of zero amplitude.
4 The matter waves are waves of probability amplitude.
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357874 The de Broglie wavelength associated with a particle of mass \(m\), moving with a velocity \(v\) and energy \(E\) is given by

1 \(h / m v^{2}\)
2 \(m v / h^{2}\)
3 \(h / \sqrt{2 m E}\)
4 \(\sqrt{2 m E} / h^{2}\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357871 The potential energy of a particle of mass \(m\) is given by
\(U(x)= \begin{cases}E_{0}: & 0 \leq x \leq 1 \\ 0 ; & x>1\end{cases}\)
\(\lambda_{1}\) and \(\lambda_{2}\) are the de Broglie wavelength of the particle, when \(0 \leq x \leq 1\) and \(x>1\) respectively. If the total energy of particle is \(2 E_{0}\), the ratio \(\dfrac{\lambda_{1}}{\lambda_{2}}\) will be

1 1
2 2
3 \(\dfrac{1}{\sqrt{2}}\)
4 \(\sqrt{2}\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357872 A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is
(Assume \(h = 6.63 \times {10^{ - 34}}Js,\) \({m_e} = 9.0 \times {10^{ - 31}}\;kg\) and \({m_p} = 1836\,\,{\text{times}}\,\,{m_e})\)

1 1:1836
2 \(1: \dfrac{1}{1836}\)
3 \(1: \sqrt{1836}\)
4 \(1: \dfrac{1}{\sqrt{1836}}\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357873 Choose the correct statement

1 Any charged particle in rest is accompanied by matter waves.
2 Any uncharged particle in rest is accompanied by matter waves.
3 The matter waves are waves of zero amplitude.
4 The matter waves are waves of probability amplitude.
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357874 The de Broglie wavelength associated with a particle of mass \(m\), moving with a velocity \(v\) and energy \(E\) is given by

1 \(h / m v^{2}\)
2 \(m v / h^{2}\)
3 \(h / \sqrt{2 m E}\)
4 \(\sqrt{2 m E} / h^{2}\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357871 The potential energy of a particle of mass \(m\) is given by
\(U(x)= \begin{cases}E_{0}: & 0 \leq x \leq 1 \\ 0 ; & x>1\end{cases}\)
\(\lambda_{1}\) and \(\lambda_{2}\) are the de Broglie wavelength of the particle, when \(0 \leq x \leq 1\) and \(x>1\) respectively. If the total energy of particle is \(2 E_{0}\), the ratio \(\dfrac{\lambda_{1}}{\lambda_{2}}\) will be

1 1
2 2
3 \(\dfrac{1}{\sqrt{2}}\)
4 \(\sqrt{2}\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357872 A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is
(Assume \(h = 6.63 \times {10^{ - 34}}Js,\) \({m_e} = 9.0 \times {10^{ - 31}}\;kg\) and \({m_p} = 1836\,\,{\text{times}}\,\,{m_e})\)

1 1:1836
2 \(1: \dfrac{1}{1836}\)
3 \(1: \sqrt{1836}\)
4 \(1: \dfrac{1}{\sqrt{1836}}\)
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357873 Choose the correct statement

1 Any charged particle in rest is accompanied by matter waves.
2 Any uncharged particle in rest is accompanied by matter waves.
3 The matter waves are waves of zero amplitude.
4 The matter waves are waves of probability amplitude.
PHXII11:DUAL NATURE OF RADIATION AND MATTER

357874 The de Broglie wavelength associated with a particle of mass \(m\), moving with a velocity \(v\) and energy \(E\) is given by

1 \(h / m v^{2}\)
2 \(m v / h^{2}\)
3 \(h / \sqrt{2 m E}\)
4 \(\sqrt{2 m E} / h^{2}\)