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JEE Main 20 July 2021 Shift 1 Solved Paper
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© examsnet.com
Question : 3
Total: 90
A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after the which one third of the material remains ? (Take ln 3 = 1.1)
[20 Jul 2021 Shift 1]
1110 years
700 years
340 years
740 years
Validate
Solution:
Given
λ
1
=
l
n
2
700
/
year,
λ
2
=
l
n
2
1400
/
year
∴
λ
n
e
t
=
λ
1
+
λ
2
=
ln
2
[
1
700
+
1
1400
]
=
3
l
n
2
1400
∕
year
Now, Let initial no. of radioactive nuclei be No.
∴
N
0
3
=
N
0
e
−
λ
n
e
t
⇒
l
n
1
3
=
−
λ
n
e
t
t
⇒
1.1
=
3
×
0.693
1400
t
⇒
t
≈
740
years
Hence option 4
© examsnet.com
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