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Recent questions tagged wave-nature-of-matter

Potential energy of a particle varies as a function of $x$ and is given as $ U(x)$ \[ \begin {bmatrix} E_{\circ} & 0 \leq x \leq 1 \\ 0 & x > 1 \end {bmatrix} \] The de-Broglie wavelengths of the particle in the region $ 0 \leq x \leq1$ and $x>1$ are $ \lambda_1$ and $ \lambda_2$ respectively. If the total energy of the particle is $2E_{\circ}$, the ratio $ \large\frac{\lambda_1}{\lambda_2}$is

asked Jan 1, 2014 by thanvigandhi_1

1 answer

Assume that the de-Broglie wave associated with an electron can form a standing wave between the atoms arranged in a one dimensional array with nodes on each of the atomic site. It is found that one such standing wave is formed if the distance between the atoms of the array is $2\: A^{\circ}$ A similar standing wave is again formed if $d$ is increased to $2.5\: A^{\circ}$ . but not for any other intermediate value of $d$. The energy of the electron is

asked Jan 1, 2014 by thanvigandhi_1

1 answer

In which of the following cases the heavier of the two particles has a smaller de-Broglie wavelength? The two particles

asked Dec 31, 2013 by thanvigandhi_1

1 answer

The energy that should be added to an electron to reduce its de-Broglie wavelength from 1nm to 0.5 nm is

asked Dec 31, 2013 by thanvigandhi_1

1 answer

We wish to see inside an atom. Assuming the atom to have a diameter of 100 pm, this means that one must be able to resolve a width of say 10 pm. If an electron microscope is used, the minimum electron energy required is about

asked Dec 31, 2013 by thanvigandhi_1

1 answer

Which of the following graphs correctly represents the variation of particle momentum with associated de-Broglie wavelength?

asked Dec 31, 2013 by thanvigandhi_1

1 answer

De Broglie used Einstein’s special theory of relatively together with Plank’s quantum theory to establish the wave property of particles. He gave fundamental relationship $ \large\frac{ \lambda h}{p}$; where $ lambda$ and $p$ are wavelength and momentum respectively and $h$ is Plank’s constant. A de-Broglie wave associated with an electron can form a standing wave between the atoms arranged in a one dimensional array with node at each of the atomic sites. A standing wave is formed when the distance between the atoms of any array is $d = 3A^{\circ}$. A similar standing wave is again formed if $d = 3.5 A^:{\circ}$ but not for any intermediate value of $d$. For thermal neutron at ordinary temperature, energy is given by relation $E = kT$, where $K$ is Boltzmann constant mass of Neutron is $1.67\times10^{–23} g$. The least value of d for which standing wave can be formed is

asked Dec 30, 2013 by thanvigandhi_1

1 answer

The quark structure of protons and neutrons appears at the minute length-scale of $10^{-15}m$ or less. This structure was first probed in early 1970’s using high energy electron beams produced by a linear accelerator at Stanford, USA. Guess the order of energy of these electron beams. (Take wavelength of a proton = $10^{-15}m$ ; rest mass of energy of electron = $0.511\: MeV$)

asked Dec 30, 2013 by thanvigandhi_1

1 answer

If the KE of a free electron doubles, its de-Broglie wavelength changes by the factor

asked Dec 28, 2013 by thanvigandhi_1

1 answer

An electron is accelerated through a potential difference of V volt. It has a wavelength $ \lambda$ associated with it. Through what potential difference must an electron be accelerated so that its de-Broglie wavelength is the same as that of a proton? Take mass of a proton to be 1837 times larger than the mass of electron.

asked Dec 27, 2013 by thanvigandhi_1

1 answer

When the momentum of a proton is changed by an amount $p_{\circ}$, the corresponding change in de- Broglie wavelength is found to be $0.25 \%$. Then, the original momentum of the proton was

asked Dec 27, 2013 by thanvigandhi_1

1 answer

If the KE of a free electron doubles, its de Broglie wavelength changes by a factor:

asked Dec 27, 2013 by thanvigandhi_1

1 answer

An electron is 2000 times lighter than a proton. Both are moving such that their matter waves have a length of $ 1\: \dot {A}$. The ratio of their kinetic energy in approximation is

asked Dec 27, 2013 by thanvigandhi_1

1 answer

De Broglie wavelength of photoelectrons is $1\: A^{\circ}$ . What is stopping potential?

asked Dec 27, 2013 by thanvigandhi_1

1 answer

In an accelerator experiment on high – energy collisions of electrons with positrons, a certain event is interpreted as annihilation of an electron – positron pair of total energy $10.2\: BeV$ into two $ \gamma$-rays of equal energy. What is the wavelength associated with each $ \gamma$-ray? $(1\; Bev = 10^9\: eV)$

asked Dec 27, 2013 by thanvigandhi_1

1 answer

Find the de Broglie $ \lambda$ of a neutron, in thermal equilibrium with matter, having an average $KE\: of \bigg(\large\frac{3}{2} \bigg)\: kT$ at $300 \: K.$

asked Dec 27, 2013 by thanvigandhi_1

1 answer

The typical de Broglie wavelength associated with a $He$ atom in $He$ gas at room temperature $(27^{\circ}C)$ and $1 \: atm$ pressure is $ \lambda$, and the mean separation between two atoms under these conditions is $r.$

asked Dec 27, 2013 by thanvigandhi_1

1 answer

What is the de Broglie wavelength of a nitrogen molecule in air at $300\; K?$ Assume molecule is moving with the rms speed of molecules at this temp. At. mass of $N= 14.0076 \; u$

asked Dec 25, 2013 by thanvigandhi_1

1 answer

The $ \lambda$ of light from the spectral emission line of sodium is $589\: nm$. Find the $KE$ at which an electron would have the same de Broglie wavelength.

asked Dec 25, 2013 by thanvigandhi_1

1 answer

Which of the following is correct?

asked Dec 24, 2013 by thanvigandhi_1

1 answer

The $KE$ of an electron with de-Broglie wavelength of $0.3\: nm$ is

asked Dec 24, 2013 by thanvigandhi_1

1 answer

Sodium and Copper have work functions $2.3\: eV\: and \: 4.5\: eV$ respectively. Then the ratio of the wavelengths is nearest to

asked Dec 24, 2013 by thanvigandhi_1

1 answer

A photodetector used to detect the wavelength of 1700 nm, has energy gap of about

asked Dec 24, 2013 by thanvigandhi_1

1 answer

An X-ray tube operates on $30\: kV$. The minimum wavelength emitted is :

asked Dec 23, 2013 by thanvigandhi_1

1 answer

Compute the typical de Broglie wavelength of an electron $(\lambda)$ in a metal at $ 27^{\circ}C$ and compare it with the mean separation between two electrons(r) in a metal which is given to be about $2 \times 10^{-10}m$

asked Dec 23, 2013 by thanvigandhi_1

1 answer

What is the de Broglie wavelength of a dust particle of mass $1 \times 10^{-9}$ kg drifting with a speed of $\;2.2 m/s$

asked Dec 23, 2013 by thanvigandhi_1

1 answer

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