Askiitians Tutor Team
Last Activity: 16 Days ago
Let's tackle your questions one by one, starting with the concept of the work function and the energy of incident photons.
Energy of Incident Photon
The work function of a photoemissive surface is the minimum energy required to remove an electron from that surface. In your case, the work function is given as 2 eV. The stopping potential is the potential difference needed to stop the emitted electrons, which is 2 V. The energy of the emitted electrons can be calculated using the equation:
Energy of emitted electrons (E) = e × V, where e is the charge of an electron (approximately 1.6 x 10-19 coulombs) and V is the stopping potential.
Substituting the values:
E = 1.6 x 10-19 C × 2 V = 3.2 x 10-19 J
To convert this energy into electron volts (eV), we use the conversion factor where 1 eV = 1.6 x 10-19 J. Thus:
E = 3.2 x 10-19 J / (1.6 x 10-19 J/eV) = 2 eV
The total energy of the incident photon (Ephoton) can be expressed as the sum of the work function and the kinetic energy of the emitted electrons:
Ephoton = Work Function + Kinetic Energy = 2 eV + 2 eV = 4 eV.
Decay of Radioactive Sample
Next, let's consider the radioactive sample. You mentioned it contains 2 x 1016 atoms. The decay process follows the half-life principle, which states that after one half-life, half of the original atoms will remain.
After a time equal to half of its half-life, the number of atoms left can be calculated as follows:
- After one half-life: 2 x 1016 / 2 = 1 x 1016 atoms remain.
- After half of the half-life: Since we are only halfway through the half-life, the number of atoms remains the same as the original amount, which is 2 x 1016 atoms.
Thus, after a decay time equal to half of its half-life, there are still 2 x 1016 atoms left uncharged.
Lateral Shift in a Glass Slab
Finally, let’s discuss the lateral shift of a ray of light incident along the normal to the surface of a glass slab. When light travels through a medium like glass, it slows down due to the medium's refractive index (n). However, if the light is incident along the normal, it does not bend at the interface; it continues straight through the slab.
The lateral shift (d) can be calculated using the formula:
d = t × (n - 1) / n
Where:
- t = thickness of the glass slab
- n = refractive index of the glass (typically around 1.5 for common glass)
Since the ray is incident along the normal, the lateral shift will be minimal. If we assume a typical refractive index of 1.5, the formula simplifies to:
d = t × (1.5 - 1) / 1.5 = t × 0.5 / 1.5 = t / 3.
Therefore, the lateral shift for a ray of light incident along the normal to the surface of a glass slab of thickness t is t/3.