A 1$\mu$ $A$ beam of protons with a cross-sectional area of $0.5$ sq. mm is moving with a velocity of $3 \times {10^4}m{s^{ - 1}}$. Then charge density of beam is

In a photoemissive cell with executing wavelength $\lambda $, the fastest electron has speed $v.$ If the exciting wavelength is changed to $\frac{{3\lambda }}{4}$, the speed of the fastest emitted electron will be

Using the Heisenberg uncertainty principle, arrange the following particles in the order of increasing lowest energy possible.

$(I)$ An electron in $H _{2}$ molecule

$(II)$ A hydrogen atom in a $H _{2}$ molecule

$(III)$ A proton in the carbon nucleus

$(IV)$ $A H _{2}$ molecule within a nanotube

When wavelength of incident photon is decreased then

The threshold wavelength for photoelectric emission from a material is $5500\,\mathring A$. Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a

$A.$ $75\,W$ infra-red lamp

$B.$ $10\,W$ infra-red lamp

$C.$ $75\,W$ ultra-violet lamp

$D.$ $10\,W$ ultra-violet lamp

Choose the correct answer from the options given below :

A photo sensitive material is at $9\,m$ to the left of the origin and the source of light is at $7\,m $ to the right of the origin along $x$ -axis. The photosensitive material and the source of light start from rest and move, respectively, with $8 \widehat i \, m / s$ and $4 \widehat i \, m / s$ . The ratio of intensities at $t = 0$ to $t = 3\,s$ as received by the photosensitive material is :-