The remaining mass of Uranium -232 has been 3.13 g. Thus, option B is correct.
The half life has been defined as the time required by the substance to reduce to half of its initial value.
The half life has been expressed as:
[tex]N_t=N_0\;(\dfrac{1}{2})^\frac{t}{t_{1/2}} [/tex]
The initial mass of uranium, [tex]N_0=100\;\rm g[/tex]
The half-life of uranium has been, [tex]t_\frac{1}{2} =68.8\;\rm years[/tex]
The time required for the reducing has been, [tex]t=344\;\rm years[/tex]
Substituting the values for the remaining mass of Uranium-232 ([tex]N_t[/tex]):
[tex]N_t=100\;\times\;(\dfrac{1}{2})^\frac{344}{68.8} \\ N_t=100\;\times\;(\dfrac{1}{2} )^5\\ N_t=3.13\;\rm g[/tex]
The remaining mass of Uranium -232 has been 3.13 g. Thus, option B is correct.
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