Question

9.
There is a stream of radioactive material having No
number of nuclei initially, moving with constant
speed of 2500 m/s. If half life of material is 693 s,
then amount of material remain after they travel a
distance of 2500 km is [NCERT]​

Answer 1

The amount of material that remains after they travel a distance of 2500 km is Ro/e.

Given:

The number of nuclei initially, moving with a constant speed of 2500 m/s. If the half-life of the material is 693 s.

To Find:

The amount of material remains after they travel a distance of 2500 km.

Solution:

To find the amount of material that remains after they travel a distance of 2500 km we will follow the following step:

$R = R o {e}^{ - kt} = R o {e}^{ - \frac{ln2}{half \: life} t} = R o {e}^{ - \frac{ln2}{693} t}$

Here, R0 is the initial number of nuclei

R is the remaining nuclei while k is the rate constant.

Now,

2500 metre travel in 1 sec.

But 2500000 metres is travelled by nuclei.

So, 2500000 metres is travelled in 1000sec.

t = 1000sec.

Now, Putting the value of t in the above equation we get,

$R = Ro {e}^{ - \frac{ln2}{693} \times 1000} =$

$R = Ro {e}^{ - \frac{0.3010 \times 2.303}{693} \times 1000} =$

$R = Ro {e}^{ - \frac{0.693}{693} \times 1000} = Ro {e}^{ - \frac{693}{693 \times 1000} \times 1000}$

$R = Ro {e}^{ - 1} = \frac{Ro}{e}$

Henceforth, the amount of material that remains after they travel a distance of 2500 km is Ro/e.

#SPJ1

Answer 2

Answer:

N/

Explanation: