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A company has the following reserves:
- Share premium: $60,000
- Revaluation reserve: $75,000
- General reserve: $10,000
- Retained earnings: $21,500
What is the maximum number of $1 bonus shares the company can issue?
A bonus issue can be made from any reserve, including capital reserves (Share Premium, Revaluation) and revenue reserves (General, Retained). Total = $60,000 + $75,000 + $10,000 + $21,500 = $166,500.
Average time between collisions $\tau$ is given by $\tau = \frac{\lambda}{v_{rms}}$, where $\lambda$ is the mean free path.
1. $\lambda \propto \frac{1}{n} \propto V$ (where $n$ is number density).
2. $v_{rms} \propto \sqrt{T}$.
3. For an adiabatic process, $TV^{\gamma-1} = \text{constant}$, so $T \propto V^{1-\gamma}$ and $\sqrt{T} \propto V^{\frac{1-\gamma}{2}}$.
Therefore, $\tau \propto \frac{V}{V^{\frac{1-\gamma}{2}}} = V^{1 - \frac{1-\gamma}{2}} = V^{\frac{2-1+\gamma}{2}} = V^{\frac{\gamma+1}{2}}$.
Hence, $q = \frac{\gamma+1}{2}$.
For \(\mu = 2.83\) BM: \(2.83 = \sqrt{n(n+2)}\) โ \(n = 2\)
Checking \(\text{Ni}^{2+}\): Ni (Z=28) = [Ar] 3dโธ 4sยฒ. \(\text{Ni}^{2+}\) = [Ar] 3dโธ โ 2 unpaired electrons โ \(\mu = \sqrt{2 \times 4} = \sqrt{8} \approx 2.83\) BM โ
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