You visited us 1 times! Enjoying our articles? Unlock Full Access!

Sub-Atomic Particles

The analysis ...

Question

The analysis of a rock shows the relative number of $^{238} U$ and $^{206} P b$ atoms $(P b / U = 0.25)$ . The age of rock will be:

\frac{2.303}{0.693} \times 4.5 \times 10^{9} log 1.25

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{2.303}{0.693} \times 4.5 \times 10^{9} log 0.25

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2.303}{0.693} \times 4.5 \times 10^{9} log 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2.303}{4.5 \times 10^{9}} \times 0.693 log 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{2.303}{0.693} \times 4.5 \times 10^{9} log 1.25$
$N_{P b} = N_{u} e^{- k t} n o w, \frac{N_{P b}}{N_{u}} + 1 = e^{- k t} = \frac{0.693}{4.5 \times 10^{9}} t = ln (\frac{N_{P b}}{N_{u}} + 1) t = \frac{2.303}{0.693} \times 4.5 \times 10^{9} log (1.25) y r s . = 3.3368 \times 10^{9}$

Suggest Corrections

Similar questions

Q. The analysis of a rock shows the relative number of

U^{238}

and

P b^{206}

atoms (Pb/U = 0.25). The age of rock will be :

Q. The number of U

^{238}

nuclei in a rock sample is equal to the number of Pb

^{206}

atoms. The half-life of U

^{238}

is 4.5 x

10^{9}

years.The age of the rock is

A sample of uranium rock from moon contains equimolar amounts of $U^{238}$ and $P b^{206}$ . The age of the rock will be $(t_{\frac{1}{2}} f o r U^{238} = 4.5 \times 10^{9} y r s)$

^{238} U

decays with a half-life of

4.5 \times 10^{9}

years, the decay series eventually ending at

^{206} P b

, which is stable. A rock sample analysis shows that the ratio of the number of atoms of

^{206} P b

^{238} U

0.0058

. Assuming that all the

^{206} P b

is produced by the decay of

^{238} U

and that all other half-lives on the chain are negligible, the age of the rock sample is

(l n 1.0058 = 5.78 \times 10^{- 3})

Q. In a sample of rock, the ratio of

^{206} P b

^{238} U

nuclei is found to be 0.5. The age of the rock is (given half-life of

U^{238}

4.5 \times 10^{9}

years)

Join BYJU'S Learning Program

The analysis of a rock shows the relative number of 238U and 206Pb atoms (Pb/U=0.25). The age of rock will be:

The correct option is A 2.3030.693×4.5×109log1.25NPb=Nue−ktnow,NPbNu+1=e−kt=0.6934.5×109t=ln(NPbNu+1)t=2.3030.693×4.5×109log(1.25)yrs.=3.3368×109

The analysis of a rock shows the relative number of $^{238} U$ and $^{206} P b$ atoms $(P b / U = 0.25)$ . The age of rock will be: