All questions of Nuclear Decay and Reactions for Grade 9 Exam

Analysis:
To answer this question, we need to understand the concept of half-life. The half-life of a radioactive substance is the time it takes for half of the initial amount of the substance to decay. In this case, the half-life of the Polonium isotope is given as 10 seconds.

Explanation:
To determine when there will no longer be any of the Polonium isotope left in the container, we can calculate the number of half-lives required for the initial 64 atoms to decay completely.

Calculations:
1. Initial number of atoms: 64
2. Half-life of Polonium isotope: 10 seconds

First half-life:
- After 10 seconds, half of the initial atoms will decay, leaving 32 atoms.

Second half-life:
- After another 10 seconds (total time = 20 seconds), half of the remaining 32 atoms will decay, leaving 16 atoms.

Third half-life:
- After another 10 seconds (total time = 30 seconds), half of the remaining 16 atoms will decay, leaving 8 atoms.

Fourth half-life:
- After another 10 seconds (total time = 40 seconds), half of the remaining 8 atoms will decay, leaving 4 atoms.

Fifth half-life:
- After another 10 seconds (total time = 50 seconds), half of the remaining 4 atoms will decay, leaving 2 atoms.

Sixth half-life:
- After another 10 seconds (total time = 60 seconds), half of the remaining 2 atoms will decay, leaving 1 atom.

Seventh half-life:
- After another 10 seconds (total time = 70 seconds), half of the remaining 1 atom will decay, leaving 0 atoms.

Conclusion:
Based on the calculations above, it can be concluded that after 70 seconds (option B), there will no longer be any of the Polonium isotope left in the container.

Understanding the Behavior of Charged Isotopes in a Magnetic Field
When charged isotopes enter a magnetic field, their behavior is influenced by both their velocity and the orientation of their motion relative to the magnetic field lines. In this scenario, where the isotopes enter the magnetic field at an angle that is neither perpendicular nor parallel, the following occurs:
Corkscrew Motion
- The isotopes experience a force due to the magnetic field, known as the Lorentz force, which acts perpendicular to both the velocity of the isotopes and the direction of the magnetic field.
- This results in a centripetal force that causes the isotopes to move in a circular path while simultaneously continuing to advance in the direction of their initial velocity.
Components of Motion
- The isotopes have two components of motion:
- Circular Motion: The isotopes curve around the magnetic field lines due to the perpendicular component of their velocity. This creates a circular path.
- Linear Motion: The isotopes continue to move forward along the direction of their initial velocity.
Resulting Path
- The combination of these two motions results in a helical or corkscrew pattern:
- As the isotopes rotate around the magnetic field lines, they also advance forward, creating a spiral trajectory.
Conclusion
- Therefore, when charged isotopes enter a magnetic field at an angle, they do not follow simple circular or elliptical paths but instead exhibit a corkscrew motion. This behavior is a direct consequence of the interplay between their velocity and the magnetic field orientation, leading to the conclusion that option 'A' is indeed correct.