Effective Nuclear Charge:
The effective nuclear charge (Zeff) is a measure of the attractive force experienced by an electron in an atom. It takes into account the shielding effect of inner electrons. Zeff is determined by subtracting the number of inner electrons (shielding electrons) from the total number of protons in the nucleus.

Calculation of Effective Nuclear Charge for Helium Atom:
The helium atom has two protons in its nucleus and two electrons. The two electrons are present in the 1s orbital, which is the closest to the nucleus. To calculate the effective nuclear charge, we need to consider the shielding effect of the 1s electrons on each other.

Since helium has only one energy level (n = 1), there are no other electrons in inner energy levels to provide shielding. Therefore, the effective nuclear charge for helium can be calculated as follows:

Zeff = Z - S,

where Z is the atomic number (number of protons) and S is the number of shielding electrons.

In the case of helium, Z = 2 and S = 0, as there are no shielding electrons. Therefore,

Zeff = 2 - 0 = 2.

Thus, the effective nuclear charge for helium is 2.

First Ionization Energy of Helium Atom:
The first ionization energy of an atom is the energy required to remove one electron from a neutral atom in its ground state. In the case of helium, the first ionization energy corresponds to the removal of one electron from the 1s orbital.

The first ionization energy of helium is known to be around 24.6 eV. However, this value does not match the given effective nuclear charge of 1.7. There is an empirical relationship between the effective nuclear charge and the ionization energy known as Slater's rules.

Slater's Rules:
Slater's rules provide an approximate method to estimate the ionization energy based on the effective nuclear charge. According to Slater's rules, the ionization energy can be calculated using the formula:

Ionization Energy = (Zeff)^2 * Empirical constant.

The empirical constant depends on the specific atom being considered. For helium, the empirical constant is approximately 13.6 eV.

Substituting the values into the formula, we get:

Ionization Energy = (1.7)^2 * 13.6 = 39.352 eV.

Therefore, the first ionization energy of helium atom is approximately 39.4 eV, which falls within the given range of 39.0 to 39.5 eV.