Which of the following atoms would have the greatest velocity if each atom had the same kinetic energy?

Ammonia? Bromine? Hydrogen? Chlorine?

Avg molecular speed = sqrt(T/molar mass)

hydrogen

To compare the velocities of different atoms, we can use the kinetic energy equation:

KE = 1/2mv^2

where KE is the kinetic energy, m is the mass of the atom, and v is the velocity.

Given that each atom has the same kinetic energy, we can compare their masses to determine which atom will have the greatest velocity. The lighter the atom, the greater its velocity for the same kinetic energy.

So, let's compare the masses of the given atoms:

Ammonia (NH3) has a molar mass of 17.031 g/mol.
Bromine (Br2) has a molar mass of 159.808 g/mol.
Hydrogen (H2) has a molar mass of 2.016 g/mol.
Chlorine (Cl2) has a molar mass of 70.906 g/mol.

Comparing the molar masses, we can see that Hydrogen (H2) has the lowest molar mass, followed by Ammonia (NH3), Chlorine (Cl2), and Bromine (Br2). Therefore, Hydrogen (H2) will have the greatest velocity of all the given atoms if they have the same kinetic energy.

To determine which atom would have the greatest velocity if each atom had the same kinetic energy, we can use the formula for kinetic energy.

The formula for kinetic energy (KE) is given by:

KE = (1/2) * m * v^2

where m is the mass of the atom and v is the velocity of the atom.

Given that each atom has the same kinetic energy, we can assume that KE is constant for all atoms:

KE_ammonia = KE_bromine = KE_hydrogen = KE_chlorine

Since the kinetic energy is constant, we can compare the velocities of the atoms to determine which one would have the greatest velocity.

Rearranging the formula for velocity (v), we have:

v = √(2 * KE / m)

Since the kinetic energy is constant, we can ignore it in the comparison and focus on the term (2 / m).

The atom with the smallest mass (m) will have the largest value for (2 / m). Therefore, the atom with the greatest velocity (v) would be the one with the smallest mass.

Looking at the options provided, we have:

Ammonia (NH3) - molecular mass = 17 g/mol
Bromine (Br) - atomic mass = 80 g/mol
Hydrogen (H) - atomic mass = 1 g/mol
Chlorine (Cl) - atomic mass = 35.5 g/mol

Comparing the masses, we see that hydrogen has the smallest mass (1 g/mol). Therefore, hydrogen would have the greatest velocity if each atom had the same kinetic energy.

So, the answer is Hydrogen.