A patient undergoing treatment for thyroid cancer receives a dose of radioactive iodine $(^{131} I)$ , which has a half-life of $8.05$ days. If the original dose contained $12 m g$ of $^{131} I$ , calculate the mass of $^{131} I$ remains after $16.1$ days?

6 m g

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

9 m g

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

2 m g

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

3 m g

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

Open in App

Solution

The correct option is B $3 m g$
Half life $t_{1 / 2} = 8.05$ days
The decay constant $λ = \frac{0.693}{t_{1 / 2}} = \frac{0.693}{8.05}$
$t = \frac{2.303}{λ} l o g \frac{a}{a - x}$

$16.1 = \frac{2.303 \times 8.05}{0.693} l o g \frac{12}{a - x}$

$a - x = 3$ mg

Suggest Corrections

Similar questions

Q. Iodine-131 is a radioactive isotope. If

1.0 m g

^{131} I

has an activity of

4.6 \times 10^{12} B q

. What is the half-life of

^{131} I

(in days)?

Q. Radioactive ¹³¹I has a half-life of 8.0 days. A sample containing ¹³¹I has activity 20 µCi at t = 0. (a) What is its activity at t = 4 days? (b) What is its decay constant at t = 4.0 days?

Radioactivity $^{131} I$ has a half-life of 8.0 days. A sample containing $^{131} I$ has activity $20 μ Ci$ (a) What is its activity at t = 4.0 days ? (b) What is its decay constant at t = 4.0 days ?

Radioactive $^{131} I$ has a half-life of $8.0$ days. A sample containing $^{131} I$ has activity $20 μ C i$ at $t = 0$ .
(a) What is its activity at $t = 4.0$ days? (b) What is its decay constant at $t = 4.0$ days?

Q. One

μ g

of a radioactive iodine contained in thyroxine is injected into the blood of a patient. How long will it take for radioactivity to fall to

50

25

% and

10

% of the initial value? (

t_{1 / 2}

for

_{53}^{131} I = 8.05

days)

Join BYJU'S Learning Program

A patient undergoing treatment for thyroid cancer receives a dose of radioactive iodine (131I), which has a half-life of 8.05 days. If the original dose contained 12mg of 131I, calculate the mass of 131I remains after 16.1 days?

The correct option is B 3mgHalf life t1/2=8.05 daysThe decay constant λ=0.693t1/2=0.6938.05t=2.303λlogaa−x16.1=2.303×8.050.693log12a−xa−x=3 mg

A patient undergoing treatment for thyroid cancer receives a dose of radioactive iodine $(^{131} I)$ , which has a half-life of $8.05$ days. If the original dose contained $12 m g$ of $^{131} I$ , calculate the mass of $^{131} I$ remains after $16.1$ days?

The correct option is B $3 m g$
Half life $t_{1 / 2} = 8.05$ days
The decay constant $λ = \frac{0.693}{t_{1 / 2}} = \frac{0.693}{8.05}$
$t = \frac{2.303}{λ} l o g \frac{a}{a - x}$

$16.1 = \frac{2.303 \times 8.05}{0.693} l o g \frac{12}{a - x}$

$a - x = 3$ mg