Estimate the speed with which electrons emitted from a heated cathode of an evacuated tube impinge on the anode maintained at a potential difference of 500 V with respect to the cathode. Ignore the small initial speeds of the electrons. The specific charge of the electron i.e., its e/m is given to be 1.76 × 1011 C kg-1

Question

Estimate the speed with which electrons emitted from a heated cathode of an evacuated tube impinge on the anode maintained at a potential difference of 500 V with respect to the cathode. Ignore the small initial speeds of the electrons. The specific charge of the electron i.e., its e/m is given to be 1.76 × 1011 C kg-1 (A) 1.33× 106 ms-1 (B) 2.66× 107 ms-1 (C) 1.33× 107 ms-1 (D) 2.66× 106 ms-1

Tardigrade Admin · Accepted Answer

Energy of accelerated electron E=500 eV Specific charge, e/m =1.76×1011C kg-1, Kinetic energy E = (1/2)mv2=eV ∴ v=√2V (e m)=√2×1.76×1011×500 =1.33×107 m s-1

$1.33 \times 1 0^{6} m s^{- 1}$

$2.66 \times 1 0^{7} m s^{- 1}$

$1.33 \times 1 0^{7} m s^{- 1}$

$2.66 \times 1 0^{6} m s^{- 1}$

Energy of accelerated electron $E = 500 e V$
Specific charge, e/m $= 1.76 \times 1 0^{11} C k g^{- 1}$ ,
Kinetic energy $E = \frac{1}{2} m v^{2} = e V$
$∴ v = 2 V (e m) = 2 \times 1.76 \times 1 0^{11} \times 500$
$= 1.33 \times 1 0^{7} m s^{- 1}$

1.33×106ms−1

2.66×107ms−1

1.33×107ms−1

2.66×106ms−1

Energy of accelerated electron E=500eV Specific charge, e/m =1.76×1011Ckg−1, Kinetic energy E=21​mv2=eV ∴v=2V(em)​=2×1.76×1011×500​ =1.33×107ms−1

$1.33 \times 1 0^{6} m s^{- 1}$

$2.66 \times 1 0^{7} m s^{- 1}$

$1.33 \times 1 0^{7} m s^{- 1}$

$2.66 \times 1 0^{6} m s^{- 1}$

Energy of accelerated electron $E = 500 e V$
Specific charge, e/m $= 1.76 \times 1 0^{11} C k g^{- 1}$ ,
Kinetic energy $E = \frac{1}{2} m v^{2} = e V$
$∴ v = 2 V (e m) = 2 \times 1.76 \times 1 0^{11} \times 500$
$= 1.33 \times 1 0^{7} m s^{- 1}$