The work functions of silver and sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for silver to that of sodium is ___________.

A proton is fired from very far away towards a nucleus with charge Q = 120e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the proton at its start is ____________. (Take the proton mass, $${m_p} = (5 \times 3) \times {10^{ - 27}}$$ kg; $$h/e = 4.2 \times {10^{ - 15}}$$ J.s/C; $${1 \over {4\pi {\varepsilon _0}}} = 9 \times {10^9}$$ m/F; 1 fm = 10¹⁵ m.)

The activity of a freshly prepared radioactive sample is 10¹⁰ disintegrations per second, whose mean life is 10⁹ s. The mass of an atom of this radioisotope is 10^$$-$$25 kg. The mass (in mg) of the radioactive sample is _________.

A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the spheres is A $$\times$$ 10^Z (where 1 < A < 10). The value of Z is _____________.