Two radioactive isotopes P and Q have half lives 10 minutes and 15 minutes respectively. Freshly prepared samples of each isotope initially contain the same number of atoms. After 30 minutes, the ratio ( textnumber of atoms of P/ textnumber of atoms of Q) will be

Question

Two radioactive isotopes P and Q have half lives 10 minutes and 15 minutes respectively. Freshly prepared samples of each isotope initially contain the same number of atoms. After 30 minutes, the ratio ( textnumber of atoms of P/ textnumber of atoms of Q) will be (A) 0.5 (B) 2.0 (C) 1.0 (D) 3.0

Tardigrade Admin · Accepted Answer

Tp=10 minute TQ=15 minute After 30 minute P has gone 3 half lives and Q=2 half lives NP=N0((1/2))3 NQ=N0((1/2))2 NP: NQ=1: 2 or (NP/NQ)=0.5

Q. Two radioactive isotopes $P$ and $Q$ have half lives $10$ minutes and $15$ minutes respectively. Freshly prepared samples of each isotope initially contain the same number of atoms. After $30$ minutes, the ratio
$\frac{number of atoms of P}{number of atoms of Q}$ will be

0.5

2.0

1.0

3.0

$T_{p} = 10$ minute
$T_{Q} = 15$ minute
After $30$ minute $P$ has gone $3$ half lives and $Q = 2$ half lives
$N_{P} = N_{0} (\frac{1}{2})^{3}$
$N_{Q} = N_{0} (\frac{1}{2})^{2}$
$N_{P} : N_{Q} = 1 : 2$
or $\frac{N _{P}}{N _{Q}} = 0.5$

Q. Two radioactive isotopes P and Q have half lives 10 minutes and 15 minutes respectively. Freshly prepared samples of each isotope initially contain the same number of atoms. After 30 minutes, the ratio number of atoms of Qnumber of atoms of P​ will be

0.5

2.0

1.0

3.0

Tp​=10 minute TQ​=15 minute After 30 minute P has gone 3 half lives and Q=2 half lives NP​=N0​(21​)3 NQ​=N0​(21​)2 NP​:NQ​=1:2 or NQ​NP​​=0.5

Q. Two radioactive isotopes $P$ and $Q$ have half lives $10$ minutes and $15$ minutes respectively. Freshly prepared samples of each isotope initially contain the same number of atoms. After $30$ minutes, the ratio
$\frac{number of atoms of P}{number of atoms of Q}$ will be

$T_{p} = 10$ minute
$T_{Q} = 15$ minute
After $30$ minute $P$ has gone $3$ half lives and $Q = 2$ half lives
$N_{P} = N_{0} (\frac{1}{2})^{3}$
$N_{Q} = N_{0} (\frac{1}{2})^{2}$
$N_{P} : N_{Q} = 1 : 2$
or $\frac{N _{P}}{N _{Q}} = 0.5$