Two electrons are moving with the same speed $v$. One electron enters a region of a uniform electric field,while the other enters a region of a uniform magnetic field. If the de-Broglie wavelengths of the two electrons after some time are ${\lambda _1}$ and ${\lambda _2}$ respectively,then:

Two parallel discs are connected by a rigid rod of length $L=0.5 \,m$ centrally. Each disc has a slit oppositely placed as shown in the figure. $A$ beam of neutral atoms is incident on one of the discs axially at different velocities $v$,while the system is rotated at an angular speed of $600 \,rev/s$,so that atoms only with a specific velocity emerge at the other end. Calculate the two largest speeds (in $m/s$) of the atoms that will emerge at the other end.

Assertion: The specific charge of positive rays is not constant.
Reason: The mass of ions varies with speed.

Assertion $(A)$: In the photoelectric effect,on increasing the intensity of light,both the number of electrons emitted and the kinetic energy of each of them increase,but the photoelectric current remains unchanged.
Reason $(R)$: The photoelectric current depends only on the wavelength of light.

In a photocell,bichromatic light of wavelengths $2475 \ \mathring{A}$ and $6000 \ \mathring{A}$ is incident on a cathode whose work function is $4.8 \ eV$. If a uniform magnetic field of $3 \times 10^{-5} \ T$ exists parallel to the plate,the radius of the path described by the photoelectron will be ............ $cm$ (mass of electron $= 9 \times 10^{-31} \ kg$).

The radiation corresponding to the $3 \rightarrow 2$ transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of $5 \times 10^{-4} \, T$. Assume that the radius of the largest circular path followed by these electrons is $7 \, mm$. The work function of the metal is $..... \, eV$. (Mass of electron $= 9.1 \times 10^{-31} \, kg$)