Question:
Rn decays into Po by emitting an \( \alpha \)-particle with half-life of 4 days. A sample contains \( 6.4 \times 10^{10} \) atoms of Rn after 12 days, the number of atoms of Rn left in the sample will be:
Rn decays into Po by emitting an \( \alpha \)-particle with half-life of 4 days. A sample contains \( 6.4 \times 10^{10} \) atoms of Rn after 12 days, the number of atoms of Rn left in the sample will be:
Show Hint
The number of atoms left after a certain time can be calculated using the half-life formula, which involves the exponential decay of the substance.
Updated On: Apr 22, 2026
- \( 3.2 \times 10^{10} \)
- \( 0.53 \times 10^{10} \)
- \( 2.1 \times 10^{10} \)
- \( 0.8 \times 10^{10} \)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Understand the decay process.
The half-life \( t_{1/2} \) of radon (\( Rn \)) is 4 days. The number of atoms of radon after time \( t \) can be calculated using the formula: \[ N(t) = N_0 \left( \frac{1}{2} \right)^{\frac{t}{t_{1/2}}} \] where \( N_0 \) is the initial number of atoms, \( N(t) \) is the number of atoms after time \( t \), and \( t_{1/2} \) is the half-life.
Step 2: Calculate the remaining atoms after 12 days.
Substitute the values into the formula: \[ N(12) = 6.4 \times 10^{10} \left( \frac{1}{2} \right)^{\frac{12}{4}} = 6.4 \times 10^{10} \times \left( \frac{1}{2} \right)^3 = 6.4 \times 10^{10} \times \frac{1}{8} = 0.8 \times 10^{10} \]
The half-life \( t_{1/2} \) of radon (\( Rn \)) is 4 days. The number of atoms of radon after time \( t \) can be calculated using the formula: \[ N(t) = N_0 \left( \frac{1}{2} \right)^{\frac{t}{t_{1/2}}} \] where \( N_0 \) is the initial number of atoms, \( N(t) \) is the number of atoms after time \( t \), and \( t_{1/2} \) is the half-life.
Step 2: Calculate the remaining atoms after 12 days.
Substitute the values into the formula: \[ N(12) = 6.4 \times 10^{10} \left( \frac{1}{2} \right)^{\frac{12}{4}} = 6.4 \times 10^{10} \times \left( \frac{1}{2} \right)^3 = 6.4 \times 10^{10} \times \frac{1}{8} = 0.8 \times 10^{10} \]
Was this answer helpful?
0
0
Top MET Physics Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- A rope of mass $0.1\, kg$ is connected at the same height of two opposite walls. It is allowed to hang under its own weight. At [he contact point between the rope and the wall, the rope makes an angle $ \theta =10^{\circ} $ with respect to horizontal. The tension in the rope at its midpoint between the walls is
- At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as
View More Questions
Top MET Decay Rate Questions
- The half-life of a radioactive element is 10 days. The time required for 75% of the element to decay is:
- A radioactive substance has a half-life of 60 min. During 3 hours, the fraction of the substance that has decayed is:
- The reaction involved in the oil of winter green test is salicylic acid + missing reagent $\xrightarrow{\Delta, \text{Conc. H}_{2}\text{SO}_{4}}$ product. The missing reagent in the above reaction is
- A covalent molecule $AB_{3}$ has pyramidal structure. The number of lone pair and bond pair of electrons in the molecule are respectively
- A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. Calculate the minimum time after which it would be possible to work safely with this source.
View More Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions