Sovi.AI - AI Math Tutor

Scan to solve math questions

QUESTION IMAGE

3. each box has 2 isotopes of the same element. fill in the isotope nam…

Question

  1. each box has 2 isotopes of the same element. fill in the isotope names and any missing information. use the isotope name convention, e.g. carbon - 14. assume neutral atom in ground state.
# of n1715# of e--10-12
# of p+25# of e-6
# of e-# of p+6
# of n
iron-iron--54-56
# of p+# of n
# of e-# of e-
# of n2730# of p+24
  1. fill in any missing information. assume neutral atom in ground state.
isotope namemass numberatomic number# of p+# of e-# of n°full nuclear notation
chromium - 5050 24 c

Explanation:

Step1: Recall atomic - related concepts

For a neutral atom in the ground state, the number of electrons (\(e^-\)) is equal to the number of protons (\(P^+\)), and the mass number (\(A\)) is the sum of the number of protons and neutrons (\(N\)). The atomic number (\(Z\)) is equal to the number of protons.

Step2: First table (left - top)

Given \(N = 17\) and \(P^+=25\). For a neutral atom, \(e^-=P^+=25\). The mass number \(A = P^++N=25 + 17=42\). The element with \(P^+=25\) is manganese. The isotope name is Manganese - 42.
For the second isotope in the first box, if \(N = 15\) and \(P^+=25\), then \(e^-=25\) and the mass number \(A=25 + 15 = 40\), isotope name is Manganese - 40.

Step3: Second table (right - top)

Given \(e^- = 6\) and \(P^+=6\), then \(N\) can be calculated from the isotope name convention. If the isotope name is not given directly, assume we are dealing with carbon (since \(P^+=6\)). For a neutral carbon atom with \(e^- = 6\) and \(P^+=6\). If the first isotope has \(e^-=6\) and \(P^+=6\), and assume mass number \(A_1\) and \(A_2\) from the given data. If \(e^- = 6\) and \(P^+=6\), for a neutral atom it is carbon. If \(N_1\) and \(N_2\) are the number of neutrons. We know \(A=P^++N\).
For the first carbon isotope, if \(e^-=6\) and \(P^+=6\), assume mass number \(A_1\) is not given directly. For the second carbon isotope, if \(e^- = 6\) and \(P^+=6\), and \(N_2\) is related to the mass - number. Since \(P^+=6\), the element is carbon. If \(e^-=6\) and \(P^+=6\), for a neutral atom, and if we assume the mass numbers from the context of isotopes, if \(N_1\) and \(N_2\) are the number of neutrons, \(A_1=P^++N_1\) and \(A_2=P^++N_2\).

Step4: Third table (left - bottom)

For iron, the atomic number of iron \(Z = 26\). For Iron - \(x\) isotopes, \(P^+=26\) for both. For the first isotope with \(N = 27\), \(e^-=26\) (neutral atom) and mass number \(A_1=26 + 27=53\), isotope name is Iron - 53. For the second isotope with \(N = 30\), \(e^-=26\) and mass number \(A_2=26+30 = 56\), isotope name is Iron - 56.

Step5: Fourth table (right - bottom)

Given \(P^+=24\), the element is chromium. For a neutral atom, \(e^-=24\). For the first isotope with mass number \(A_1 = 54\), \(N_1=A_1 - P^+=54 - 24=30\). For the second isotope with mass number \(A_2 = 56\), \(N_2=A_2 - P^+=56 - 24=32\).

Step6: Fifth table (question 4)

For Chromium - 50:
The atomic number of chromium \(Z = 24\), so \(P^+=24\). For a neutral atom, \(e^-=24\). The mass number \(A = 50\), and \(N=A - P^+=50 - 24=26\). The full nuclear notation is \(_ {24}^{50}Cr\).
For the second isotope, given \(P^+=14\), the element is silicon. The atomic number \(Z = 14\), for a neutral atom \(e^-=14\). Given \(N = 17\), the mass number \(A=P^++N=14 + 17=31\). The isotope name is Silicon - 31, and the full nuclear notation is \(_ {14}^{31}Si\).

Answer:

Isotope NameMass NumberAtomic Number# of \(P^+\)# of \(e^-\)# of \(N\)Full Nuclear Notation
Manganese - 404025252515\(_ {25}^{40}Mn\)
Carbon - (unknown mass - 1)-666(unknown)\(_ {6}^{A_1}C\)
Carbon - (unknown mass - 2)-666(unknown)\(_ {6}^{A_2}C\)
Iron - 535326262627\(_ {26}^{53}Fe\)
Iron - 565626262630\(_ {26}^{56}Fe\)
Chromium - 545424242430\(_ {24}^{54}Cr\)
Chromium - 565624242432\(_ {24}^{56}Cr\)
Chromium - 505024242426\(_ {24}^{50}Cr\)
Silicon - 313114141417\(_ {14}^{31}Si\)