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alexandr1967 [171]
3 years ago
15

) A coin is tossed 13 times. a) How many different outcomes are possible? 2^8 b) How many different outcomes have exactly 4 head

s? 70 c) How many different outcomes have at least 2 heads ? 247 d) How many different outcomes have at most 4 heads? 163
Physics
1 answer:
Svetradugi [14.3K]3 years ago
3 0

Answer:

Explanation:

a) A coin has two sides, therefore the total outcome possible when a coin is tossed is 2 i.e Head (H) and Tail (T)

outcome of two coins will be 4 i.e 2^2

Outcome of three coins will be 8 i.e 2^3 and so on. Since its following a trend, the outcome when 'n' coins is tossed will be 2^n.

Using the general formula, the possible outcome when a coin is tossed 13 times will be "2^13"

b)

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slega [8]

Answer:

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There are two half-reactions in this question. \rm Cu^{2+} + 2\,e^{-} \rightleftharpoons Cu and \rm Pb^{2+} + 2\,e^{-} \rightleftharpoons Pb. Either could be the cathode (while the other acts as the anode.) However, for the reaction to be spontaneous, the value of E^{\circ}(\text{cell}) should be positive.

In this case, E^{\circ}(\text{cell}) is positive only if \rm Cu^{2+} + 2\,e^{-} \rightleftharpoons Cu is the reaction takes place at the cathode. The net reaction would be

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Its cell potential would be equal to 0.339 - (-0.130) = \rm 0.469\; V.

The maximum amount of electrical energy possible (under standard conditions) is equal to the free energy of this reaction:

\Delta G^{\circ} = n \cdot F \cdot E^{\circ} (\text{cell}),

where

  • n is the number moles of electrons transferred for each mole of the reaction. In this case the value of n is 2 as in the half-reactions.
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\begin{aligned}\Delta G^{\circ} &= n \cdot F \cdot E^{\circ} (\text{cell})\cr &= 2\times 96485.33212 \times (0.339 - (-0.130)) \cr &\approx 9.0 \times 10^{4} \; \rm J \cr &= 90\; \rm kJ\end{aligned}.

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