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Which sub-shell does not exist?
For n=1, l can be 0 only (s orbital). 1p would require l=1, not possible. 1s exists; 5d and 6f exist for higher n.
The total of Konrad's purchases ledger balances was $57,400. Later, these errors were found:
| Discount allowed overcast in cash book | $2,000 |
| Returns outwards omitted in a supplier's account | $350 |
| Payments to trade payables undercast in cash book | $137 |
| Purchases journal overcast | $500 |
What is the corrected total of the trade payables balances?
Only errors affecting individual supplier accounts change the purchases ledger total.
1. Returns outwards omitted: $57,400 - $350 = $57,050.
The others (Discount allowed, payments undercast in cash book, journal overcast) affect the Control Account or other ledgers, but not the individual ledger balances until corrected there.
Endospores are produced by which type of bacteria?
Endospores are formed by Gram-positive bacteria like Bacillus and Clostridium. Mycobacteria are acid-fast; most Gram-negative do not form endospores.
Average collision time $\tau = \frac{\lambda}{v_{rms}}$.
Mean free path $\lambda \propto \frac{1}{n} \propto V$.
Root mean square velocity $v_{rms} \propto \sqrt{T}$.
For an adiabatic process, $T \propto V^{-(\gamma-1)}$. So, $v_{rms} \propto V^{-\frac{\gamma-1}{2}}$.
Therefore, $\tau \propto \frac{V}{V^{-\frac{\gamma-1}{2}}} = V^{1 + \frac{\gamma-1}{2}} = V^{\frac{\gamma+1}{2}}$.
Thus, $q = \frac{\gamma+1}{2}$.
Planck's constant ($h$), speed of light in vacuum ($c$), and Newton's gravitational constant ($G$) are taken as fundamental constants. Which combination of these has the dimension of length?
This is the Planck length $\ell_P = \sqrt{\dfrac{\hbar G}{c^3}}$ (with $h$ in place of $\hbar$ up to a constant).
Dimensions: $[h] = ML^2T^{-1}$, $[G] = M^{-1}L^3T^{-2}$, $[c] = LT^{-1}$
$\left[\dfrac{hG}{c^3}\right] = \dfrac{ML^2T^{-1} \cdot M^{-1}L^3T^{-2}}{L^3T^{-3}} = \dfrac{L^5T^{-3}}{L^3T^{-3}} = L^2$
$\Rightarrow \sqrt{\dfrac{hG}{c^3}} \sim [L]$ ✓
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