Question

Iridium-192 is one radioisotope used in brachytherapy in which a radioactive source is placed inside a patient's body to treat cancer. brachytherapy allows the use of a higher than normal dose to be placed near the tumor while lowering the risk of damage to healthy tissue. iridium-192 is often used in the head or breast. if a sample of iridium-192 is initially 3.25g and 1.21g remains after 105 days, estimate the half-life of the radioisotope.

Answer 1

Answer is: the half-life of the radioisotope is 74 days.
m₀ = 3.25 g.
m₁ = 1.21 g.
t = 105 d.
ln(m₀/m₁) = k· t.
ln(3.25/1.21) = k·105 d.
ln(2.685) = 105·k.
0.98 = 105k.
k = 0.0094.
t1/2 = ln2 / k.
t1/2 = 0.693 / 0.0094.
t1/2 = 73.72 days.

Answer 2

The half-life of the radioisotope : 73.68 days

Further explanation

The core reaction is a reaction that causes changes in the core structure.

In the core reaction, the number of atomic numbers and mass numbers of the reactants is the same as the atomic number and mass number of the product

Radioactivity is the process of unstable isotopes to stable isotopes by decay, by emitting certain particles, among others

• alpha α particles ₂He⁴
• beta β ₋₁e⁰ particles
• gamma particles γ
• positron particles ₁e⁰

General formulas used in decay:

$\large {\boxed {Nt=No(\frac {1} {2})^{\frac {T} {t1 / 2}}}}$

T = duration of decay

t 1/2 = half-life

No = the number of initial radioactive atoms

Nt = the number of radioactive atoms left after decaying during T time

A sample of iridium-192 is initially 3.25 g and 1.21 g remains after 105 days, estimate the half-life of the radioisotope

So :

No = 3.25 g

Nt = 1.21 g

T = 105 days

We input this to equation to find half life ($\displaystyle t\frac{1}{2}$

$\displaystyle Nt=No(\frac {1} {2})^{\frac {T} {t\frac{1}{2}}$

$\displaystyle 1.21=3.25(\frac {1} {2})^{\frac {105} {t\frac{1}{2}}$

$\displaystyle 0.372=(\frac{1}{2})^{\frac{105}{t\frac{1}{2} }$

$\displaystyle log~0.372=\frac{105}{t\frac{1}{2} }.log~0.5\\\\-0.429=\frac{105}{t\frac{1}{2} }.-0.301\\\\1.425=\frac{105}{t\frac{1}{2} }\\\\t\frac{1}{2}=\boxed{\bold{73.68~days}}$

Learn more

exponential decay

brainly.com/question/6565665

nuclear decay reaction

brainly.com/question/4207569

Plutonium − 239

brainly.com/question/10125168

 

Keywords: the half-life, decay reaction,  iridium-192