A proton and an \(\alpha\text{-}\)$$particle are accelerated from rest to the same energy. The de-Broglie wavelength \(\lambda_p\) and \(\lambda_\alpha\)${}_{}$ are in the ratio:
1. \(2:1\)
2. \(1:1\)
3. \(\sqrt{2}:1\)
4. \(4:1\)

The work function of the photosensitive material is \(4.0~\text{eV}\). The longest wavelength of light that can cause photoelectric emission from the substance is (approximately):
1. \(3100~\text{nm}\)
2. \(966~\text{nm}\)
3. \(31~\text{nm}\)
4. \(310~\text{nm}\)

A plane electromagnetic wave of wave intensity 6 W/$m^2$ strikes a small mirror of area 30 $c{m}^2$, held perpendicular to the approaching wave. The momentum transferred in kg $m{s}^{-1}$ by the wave to the mirror each second will be

(1) $1.2\times {10}^{-10}$

(2) $2.4\times {10}^{-9}$

(3) $3.6\times {10}^{-8}$

(4) $4.8\times {10}^{-7}$

An electron is accelerated through a potential difference of \(10,000~\text{V}\). Its de-Broglie wavelength is, (nearly):
\(\left(m_e = 9\times 10^{-31}~\text{kg}\right )\)
1. \(12.2~\text{nm}\)
2. \(12.2\times 10^{-13}~\text{m}\)
3. \(12.2\times 10^{-12}~\text{m}\)
4. \(12.2\times 10^{-14}~\text{m}\)

The momentum of a photon of energy 1 MeV in kg m/s, will be:

1. $0.33\times {10}^6$

2. $7\times {10}^{-24}$

3. ${10}^{-22}$

4. $5\times {10}^{-22}$

When photons of energy h$\nu$ fall on an aluminium plate (of work function E₀), photoelectrons of maximum kinetic energy K are ejected. If the frequency of the radiation is doubled, the maximum kinetic energy of the ejected photoelectrons will be:

1. $K+E_0$

2. 2K

3. K

4. K+h$\nu$

A photocell employs a photo-electric effect to convert:

Monochromatic light of frequency 6.0×10¹⁴ Hz is produced by a laser. The power emitted is 2×10^-3 W. The number of photons emitted, on average, by the source per second is:

1. $5\times {10}^{15}$

2. $5\times {10}^{16}$

3. $5\times {10}^{17}$

4. $5\times {10}^{14}$