Question

Indicate the number of protons and neutrons in the following nuclei: (a) \({ }_{25}^{55} \mathrm{Mn}\), (b) \({ }^{201} \mathrm{Hg}\), (c) potassium-39.

Short answer

In \({}_{25}^{55} \mathrm{Mn}\), there are 25 protons and 30 neutrons. In \({}^{201} \mathrm{Hg}\), there are 80 protons and 121 neutrons. In potassium-39, there are 19 protons and 20 neutrons.

Step-by-step solution

(a) Identify atomic number and mass number for \({}_{25}^{55} \mathrm{Mn}\)

In this case, the nucleus is given as \({}_{25}^{55} \mathrm{Mn}\). The subscript 25 represents the atomic number, which is the number of protons, and the superscript 55 represents the mass number, which is the total number of protons and neutrons. So, we have: Atomic number (number of protons) = 25 Mass number (number of protons + number of neutrons) = 55

(a) Calculate the number of neutrons for \({}_{25}^{55} \mathrm{Mn}\)

Now we can find the number of neutrons by subtracting the number of protons from the mass number: Number of neutrons = Mass number - Atomic number Number of neutrons = 55 - 25 Number of neutrons = 30 So, in this nucleus of Mn, there are 25 protons and 30 neutrons.

(b) Identify atomic number and mass number for \({}^{201} \mathrm{Hg}\)

In this case, the nucleus is given as \({}^{201} \mathrm{Hg}\). The mass number is given as 201, but the atomic number is not directly provided. We can, however, look up the atomic number for Hg (mercury) in the periodic table. The atomic number of mercury is 80. So, we have: Atomic number (number of protons) = 80 Mass number (number of protons + number of neutrons) = 201

(b) Calculate the number of neutrons for \({}^{201} \mathrm{Hg}\)

Now we can find the number of neutrons by subtracting the number of protons from the mass number: Number of neutrons = Mass number - Atomic number Number of neutrons = 201 - 80 Number of neutrons = 121 So, in this nucleus of Hg, there are 80 protons and 121 neutrons.

(c) Identify atomic number and mass number for potassium-39

In this case, we are given "potassium-39", which means that it is a potassium nucleus with a mass number of 39. We can find the atomic number for potassium (K) in the periodic table, which is 19. So, we have: Atomic number (number of protons) = 19 Mass number (number of protons + number of neutrons) = 39

(c) Calculate the number of neutrons for potassium-39

Now we can find the number of neutrons by subtracting the number of protons from the mass number: Number of neutrons = Mass number - Atomic number Number of neutrons = 39 - 19 Number of neutrons = 20 So, in this nucleus of potassium, there are 19 protons and 20 neutrons.