Chemistry, 27.09.2019 04:00 kutie543

Aradioactive isotope has a half-life of 10 years. what fraction of the original mass will remain unchanged after 50 years

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The fraction of the original mass of the radioactive isotope with a half-life of 10 years that will remain after 50 years is 1/32.

We can find the fraction of the original mass with the exponential decay equation:

$N(t) = N_{0}e^{-\lambda t}$ (1)

Where:

N(t): is the amount of radioactive isotope at time t

N₀: is the initial amount of radioactive isotope

λ: is the decay constant

t: is the time = 50 y

We can find the decay constant as follows:

$\lambda = \frac{ln(2)}{t_{1/2}}$ (2)

Where:

$t_{1/2}$ : is the half-life of the isotope = 10 y

The decay constant is (eq 2):

$\lambda = \frac{ln(2)}{t_{1/2}} = \frac{ln(2)}{10 y} = 0.069 y^{-1}$

Now, the fraction of the original amount is (eq 1):

$\frac{N(t)}{N_{0}} = e^{-\lambda t} = e^{-0.069 y^{-1}*50 y} = 0.0317$

Since we need to calculate the fraction of the original mass, after some algebraic operations we have:

$\frac{N_{0}}{N(t)} = 32$

$N(t) = \frac{1}{32}N_{0}$

Therefore, the fraction of the original mass that will remain is 1/32.

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Answer from: timthaartist

The fraction is calculated like this:

$\frac{1}{ {2}^{50 \div 10} } = \frac{1}{32}$

If you want an universal equation for all problems like this:

$\frac{1}{ {2}^{time \div halflife} }$

$Aradioactive isotope has a half-life of 10 years. what fraction of the original mass will remain unc$

Answer from: Quest

explanation:

metals have excess of electrons whereas non-metals have deficiency of electrons. thus, in order to gain stability metals easily donate their electrons to the non-metals.

for example, electronic configuration of sodium is $1s^{2}2s^{2}2p^{6}3s^{1}$ and electronic configuration of phosphorous is $1s^{2}2s^{2}2p^{6}3s^{2}3p^{3}$ .

when a phosphorous atom and sodium atom combine together then sodium will donate is extra one electron to the phosphorous atom. as a result there will be formation of ionic bond between sodium and phosphorous.

the reaction will be as follows.

$3na + p \rightarrow na_{3}p$

there, are three sodium sodium atoms and each of them will donate its one extra electron to phosphorous atom. thus, the sub-shell of phosphorous gets completely filled.

thus, we can conclude that electrons are transferred from atoms of sodium to atoms of phosphorous. this transfer makes the sodium atoms donate one electron and the phosphorous atoms to gain one electron. as a result, the sodium and phosphorus atoms strongly attract each other.

Electrons are transferred from atoms of to atoms of this transfer makes the sodium atoms and the

Answer from: Quest

The correct answer is b

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