The magnitude of electric field intensity that balances the weight of an α-particle is [Take, mass of proton, mp=1.67 × 10-27 kg, g=10 m / s 2 and e=1.6 × 10-19 C ]

Question

The magnitude of electric field intensity that balances the weight of an α-particle is [Take, mass of proton, mp=1.67 × 10-27 kg, g=10 m / s 2 and e=1.6 × 10-19 C ] (A) 3.3 × 10-6 N / C (B) 4.2 × 10-8 N / C (C) 2.5 × 10-9 N / C (D) 2.1 × 10-7 N / C

Tardigrade Admin · Accepted Answer

For equilibrium of α-particle, q E=m g ⇒ E=(m g/q) =(4 mp ⋅ g/2 e)=(4 × 167 × 10-27 × 10/2 × 1.6 × 10-19) =2.1 × 10-7 N / C

Q. The magnitude of electric field intensity that balances the weight of an $α$ -particle is
[Take, mass of proton, $m_{p} = 1.67 \times 1 0^{- 27} k g$ , $g = 10 m / s^{2}$ and $e = 1.6 \times 1 0^{- 19} C$ ]

$3.3 \times 1 0^{- 6} N / C$

$4.2 \times 1 0^{- 8} N / C$

$2.5 \times 1 0^{- 9} N / C$

$2.1 \times 1 0^{- 7} N / C$

For equilibrium of $α$ -particle,
$qE = m g$
$\Rightarrow E = \frac{m g}{q}$
$= \frac{4 m _{p} \cdot g}{2 e} = \frac{4 \times 167 \times 1 0 ^{- 27} \times 10}{2 \times 1.6 \times 1 0 ^{- 19}}$
$= 2.1 \times 1 0^{- 7} N / C$

Q. The magnitude of electric field intensity that balances the weight of an α-particle is [Take, mass of proton, mp​=1.67×10−27kg, g=10m/s2 and e=1.6×10−19C ]

3.3×10−6N/C

4.2×10−8N/C

2.5×10−9N/C

2.1×10−7N/C