Consider the solar system as a large atom. The quantum number (n) that characterises Earth’s orbit (radius = 1.5 × 10¹¹ m) with Earth moving at an orbital speed of 3 × 10⁴ m/s is (mass of Earth is 6 × 10²⁴ kg):

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Consider the solar system as a large atom. The quantum number (n) that characterises Earth’s orbit (radius = 1.5 × 10¹¹ m) with Earth moving at an orbital speed of 3 × 10⁴ m/s is (mass of Earth is 6 × 10²⁴ kg):

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2.56 × 10⁷⁴
2.56 × 10³⁹
2.56 × 10⁷³
2.56

Answer 1

Given:

Radius of Earth's orbit r = 1.5 × 1011 m

Mass of Earth m=6 × 1024 kg

Orbital speed Earth v=3 × 104 m/s

Concept:

The Bohr's model was based on principle of quantization of energy and angular momentum. According to Bohr's model, the momentum is quantized i.e. the angular momentum of the electron is an integer multiple of \(\frac{h}{2\pi}\).

\(mvr=\frac{nh}{2\pi}\)

Explanation:

Substitute all values in above formula , we get,

\(mvr=\frac{nh}{2\pi}\)

\(n=\frac{2\pi mvr}{h}\)

\(n=\frac{2\times3.14\times6\times10^{24}\times3\times10^4\times1.5\times10^{11}}{6.626\times10^{-34}}\)

\(n=25.61\times10^{73}=2.56\times10^{74}\)

Hence, the correct answer is Option-1-\(n=2.56\times10^{74}\).

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Consider the solar system as a large atom. The quantum number (n) that characterises Earth’s orbit (radius = 1.5 × 10¹¹ m) with Earth moving at an orbital speed of 3 × 10⁴ m/s is (mass of Earth is 6 × 10²⁴ kg):

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Consider the solar system as a large atom. The quantum number (n) that characterises Earth’s orbit (radius = 1.5 × 1011 m) with Earth moving at an orbital speed of 3 × 104 m/s is (mass of Earth is 6 × 1024 kg):

Answer (Detailed Solution Below)

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Consider the solar system as a large atom. The quantum number (n) that characterises Earth’s orbit (radius = 1.5 × 10¹¹ m) with Earth moving at an orbital speed of 3 × 10⁴ m/s is (mass of Earth is 6 × 10²⁴ kg):