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musickatia [10]
2 years ago
15

he first excited state of the helium atom lies at an energy 19.82 eV above the ground state. If this excited state is three-fold

degenerate while the ground state is non-degenerate, find the relative populations of the first excited and the ground states for helium gas in thermal equilibrium at 10,000 K.
Physics
1 answer:
bekas [8.4K]2 years ago
5 0

Answer:

Relative population is  2.94 x 10⁻¹⁰.

Explanation:

Let N₁ and N₂ be the number of atoms at ground and first excited state of helium respectively and E₁ and E₂ be the ground and first excited state energy of helium respectively.

The ratio of population of atoms as a function of energy and temperature is known as Boltzmann Equation. The equation is:

\frac{N_{1} }{N_{2} } =  \frac{g_{1}e^{\frac{-E_{1} }{KT} }  }{g_{2}e^{\frac{-E_{2} }{KT} }}

\frac{N_{1} }{N_{2} } = \frac{g_{1}e^{\frac{-(E_{1}-E_{2})  }{KT} }  }{g_{2}}

Here g₁ and g₂ be the degeneracy at two levels, K is Boltzmann constant and T is equilibrium temperature.

Put 1 for g₁, 3 for g₂, -19.82 ev for (E₁ - E₂) and 8.6x10⁵ ev/K for K and 10000 k for T in the above equation.

\frac{N_{1} }{N_{2} } = \frac{1\times e^{\frac{-(-19.82)}{8.6\times 10^{-5}\times 10000} }  }{3}

\frac{N_{1} }{N_{2} } = 3.4 x 10⁹

\frac{N_{2} }{N_{1} } =  2.94 x 10⁻¹⁰

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Answer with Explanation:

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2 years ago
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Answer:

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Step 1 : Data given

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Step 2:

⇒ Before the load falls off, thrust (T) balances the component of total weight downhill:

T = (m1+m2)*g*sinθ

⇒ After the load falls off, thrust (T) remains the same but downhill component of weight becomes  m1*gsinθ .

Resultant force on truck is F = T – m1*gsinθ  

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m1*g*sinθ + m2*g*sinθ =m1*a + m1*g*sinθ

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