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# 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 $\begin {array} {1 1} (a)\;3 \: A^{\circ} & \quad (b)\;0.5\: A^{\circ} \\ (c)\;1\: A^{\circ} & \quad (d)\;1.5\: A^{\circ} \end {array}$ Comment
A)
Ans : (b)
The min distance for which the standing wave would be formed would be equal
to the min difference between the atomic spacings, which is $0.5\: A^{\circ}$
An experimental set up for the photoelectric effect is shown in fig.1. Here, the
voltage across the electrodes (A and C) is measured with the help of ideal
voltmeter V. The voltage across the electrodes can be varied by moving
jockey J on the rheostat working as potential dividing arrangement.
The battery used in potential dividing arrangement is 10 V and its internal
resistance is 1 $\Omega$. The resistance of rheostat wire is 4$\Omega$
and its length is 50 cm. The two electrodes in vacuum tubes are plates of
platinum. The plate C is coated with potassium oxide. Each plate is of area
50 cm2 at separation of 0.5 mm. When radiations of suitable frequency or
wavelength fall on plate C, the photoelectric effect is set up which is measured
with the help of ideal ammeter. The photoelectric current in circuit is very small
so we can treat potential dividing circuit as an independent circuit.
The wavelengths of various colors are:

 Light Violet Blue Green Yellow Orange Red $\lambda$ in $A^{\circ}$ 4000-5000 5000-4000 5000-5500 5500-6000 6000-6600 6600-7800