A hydrogen nucleus has a radius of 1.1 x 10-15 m and the electron is about 5.5 x

Question

A hydrogen nucleus has a radius of 1.1 x 10-15 m and the electron is about 5.5 x 10-11 m from the nucleus. Assume the hydrogen atom is a ball with a radius of about 5.5 x 10-11 m and the nucleus is a ball with a radius of 1.1 x 10-15 m.

(a) What is the volume of the atom?
(b) What is the volume of the nucleus?
(c) What percentage of the atom is occupied by the nucleus?
d) How much work (in electron volts) must be performed by an external force to bring in another proton (from very far away) to the "surface" of the nucleus? (Ignore the effects of the electron.)

Explanation / Answer

(a) the volume of the atom V = 4/3r^3      here r = 5.5*10^-11 m      = 4/3*3.142*(166.375)*10^-33      = 697.0*10^-33 m^3 (b) the volume of the nucleus V = 4/3r^3      here r = 1.1*10^-15 m      = 4/3*3.142*(1.331)*10^-45      =  5.576*10^-45 m^3 (c) the % of the volume occupied by the nucleus
V2/V1 * 100 = 5.576*10^-45 m^3/ 697.0*10^-33 m^3*100                      = 0.8*10^-12 % (d) The distance the proton has to travel to reach the surface of the nucleus is equal to the wavelength and its value is =(55000 - 1.1) x 10-15m=54998.9 x10-15m. The work done in electron volts is E=hc/=6.626 x10-34 x 3 x 108/54998.9 x 10-15 E=3.614 x 10-15J    the volume of the nucleus V = 4/3r^3      here r = 1.1*10^-15 m      = 4/3*3.142*(1.331)*10^-45      =  5.576*10^-45 m^3 (c) the % of the volume occupied by the nucleus
V2/V1 * 100 = 5.576*10^-45 m^3/ 697.0*10^-33 m^3*100                      = 0.8*10^-12 % (d) The distance the proton has to travel to reach the surface of the nucleus is equal to the wavelength and its value is =(55000 - 1.1) x 10-15m=54998.9 x10-15m. The work done in electron volts is E=hc/=6.626 x10-34 x 3 x 108/54998.9 x 10-15 E=3.614 x 10-15J    The distance the proton has to travel to reach the surface of the nucleus is equal to the wavelength and its value is =(55000 - 1.1) x 10-15m=54998.9 x10-15m. The work done in electron volts is E=hc/=6.626 x10-34 x 3 x 108/54998.9 x 10-15 E=3.614 x 10-15J    E=3.614 x 10-15J   

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.