Question

5. In a hydrogen atom, the electron revolves round the
proton in a circular orbit of radius 0.528 Å with a speed of 2.18 x 10^6 m/s. Calculate the centripetalforce acting on the electron. ​

Answer 1

Answer:-

$\red{\bigstar}$ Centripetal Force $\large\leadsto\boxed{\rm\purple{8.2 \times 10^{-8} N}}$

• Given:-

Electron revolves around the proton in circular orbit of radius 0.528 Å

Speed of electron is 2.18 × 10^6 m/s

• To Find:-

Centripetal force acting on the electron.

• Solution:-

We know,

$\blue{\bigstar}$ $\large\underline{\boxed{\bf\pink{F = \dfrac{mv^2}{r}}}}$

where,

F = Force

m = mass of the electron

v = speed of the electron

r = radius of its orbit

We know,

• Mass of electron = 9.1 × 10-³¹ kg

• 1 Å = 10^10 m

• Substituting in the values:-

$\sf \implies F = \dfrac{9.1 \times 10^{-31} \times (2.18 \times 10^6)^2}{0.528 \times 10^{-10}}$

$\\ \sf \implies F = \dfrac{9.1 \times 10^{-31} \times 4.7524 \times 10^{12}}{0.528 \times 10^{-10}}$

$\\ \sf \implies F = 17.235 \times 10^{-21} \times 4.7524 \times 10^{12}$

$\\ \sf \implies F = 81.907 \times 10^{-9}$

$\\ \sf \implies F = 82 \times 10^{-9}$

★ $\boxed{\bf\red{F = 8.2 \times 10^{-8} N}}$

Therefore, the centripetal force acting on the electron is 8.2 × 10^-8 N.

Answer 2

$\huge{\boxed{\rm{\red{Answer}}}}$

${\bigstar}\large{\boxed{\sf{\pink{Given \: that}}}}$

• Electron revolves around the proton in circular orbit of radius 0.528 Å
• Speed of electron is 2.18 × 10^6 m/s

${\bigstar}\large{\boxed{\sf{\pink{To \: find}}}}$

• Centripetal force acting on the electron.

${\bigstar}\large{\boxed{\sf{\pink{Solution}}}}$

We know that,

• mv²

In this,

• f = Force
• m = mass of the electron
• v = speed of the electron
• r = radius of its orbit

We know that,

• Mass of electron = 9.1 × 10-³¹ kg
• 1 Å = 10^10 m

${\bigstar}\large{\boxed{\sf{\pink{Substituting \: the \: values}}}}$

• 9.1 × 10-³¹ × (2.18 × 10⁶ )² / 0.528 × 10-¹⁰
• 9.1 × 10-³¹ × 7524 × 10¹² / 0.528 × 10-¹⁰
• 17.235 × 10-²¹ × 7524 × 10¹²
• 81.907 × 10⁹
• 81 × 10⁹
• F=8.2×10-⁸N

Therefore, the centripetal force acting on the electron is 8.2 × 10^-8 N.

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