To calculate the bandgap energy of a CdSe/ZnS core/shell quantum dot with a radius of 2.5 nm, we need to consider both the bulk bandgap energy and the confinement energies of electrons and holes. We will use the effective mass approximation to calculate the confinement energies.1. Bulk bandgap energy:The bulk bandgap energy of CdSe is approximately 1.74 eV.2. Confinement energies:Using the effective mass approximation, the confinement energy for electrons Ee and holes Eh can be calculated using the following formula:E = h^2 / 8 * R^2 * 1/meff where h is the Planck's constant 6.626 x 10^-34 Js , R is the radius of the quantum dot 2.5 nm = 2.5 x 10^-9 m , and meff is the effective mass of the electron or hole.For CdSe, the effective mass of electrons me is approximately 0.13 times the mass of a free electron me0 = 9.109 x 10^-31 kg , and the effective mass of holes mh is approximately 0.45 times me0.meff_e = 0.13 * me0 = 1.184 x 10^-31 kgmeff_h = 0.45 * me0 = 4.099 x 10^-31 kgNow, we can calculate the confinement energies for electrons and holes:Ee = 6.626 x 10^-34 ^2 / 8 * 2.5 x 10^-9 ^2 * 1 / 1.184 x 10^-31 = 0.242 eVEh = 6.626 x 10^-34 ^2 / 8 * 2.5 x 10^-9 ^2 * 1 / 4.099 x 10^-31 = 0.071 eV3. Total bandgap energy:The total bandgap energy of the CdSe/ZnS core/shell quantum dot is the sum of the bulk bandgap energy and the confinement energies:E_total = E_bulk + Ee + Eh = 1.74 + 0.242 + 0.071 = 2.053 eV4. Bohr radius:The Bohr radius aB can be calculated using the following formula:aB = 4 * * * 0 * h^2 / e^2 * meff where is the relative permittivity of the material approximately 10.6 for CdSe , 0 is the vacuum permittivity 8.854 x 10^-12 F/m , and e is the elementary charge 1.602 x 10^-19 C .aB_e = 4 * * 10.6 * 8.854 x 10^-12 * 6.626 x 10^-34 ^2 / 1.602 x 10^-19 ^2 * 1.184 x 10^-31 = 6.67 nmaB_h = 4 * * 10.6 * 8.854 x 10^-12 * 6.626 x 10^-34 ^2 / 1.602 x 10^-19 ^2 * 4.099 x 10^-31 = 1.84 nmThe Bohr radius for electrons is larger than the size of the quantum dot 2.5 nm , while the Bohr radius for holes is smaller. This indicates that the quantum confinement effect is stronger for electrons than for holes in this CdSe/ZnS core/shell quantum dot.In conclusion, the bandgap energy of the CdSe/ZnS core/shell quantum dot with a radius of 2.5 nm is approximately 2.053 eV. The Bohr radius for electrons 6.67 nm is larger than the quantum dot size, while the Bohr radius for holes 1.84 nm is smaller, indicating a stronger quantum confinement effect for electrons.