Chapter 27. Binding energy of a nucleus (27-2)

Question

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Question

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{"title":"Binding energy of a nucleus","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"2,12,17,31\"}]"} {"title":"Number of neutrons in the nucleus","description":"Correct!","type":"correct","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"56,11,77,33\"}]"} {"title":"Number of protons in the nucleus","description":"Incorrect","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"130,12,148,32\"}]"} {"title":"Mass of a neutral atom (including electrons) containing that nucleus","description":"Incorrect","type":"incorrect","color":"#ff0000","code":"[{\"shape\":\"rect\",\"coords\":\"214,14,237,32\"}]"} {"title":"Speed of light in a vacuum","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"281,15,294,33\"}]"} {"title":"Mass of a neutral hydrogen atom (1 proton + 1 electron","description":"Incorrect","type":"incorrect","color":"#ff6600","code":"[{\"shape\":\"rect\",\"coords\":\"148,16,169,32\"}]"} {"title":"Mass of a neutron","description":"Incorrect","type":"incorrect","color":"#0000ff","code":"[{\"shape\":\"rect\",\"coords\":\"76,15,97,31\"}]"}

Question

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{"title":"Binding energy of a nucleus","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"2,12,17,31\"}]"} {"title":"Number of neutrons in the nucleus","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"56,11,77,33\"}]"} {"title":"Number of protons in the nucleus","description":"Correct!","type":"correct","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"130,12,148,32\"}]"} {"title":"Mass of a neutral atom (including electrons) containing that nucleus","description":"Incorrect","type":"incorrect","color":"#ff0000","code":"[{\"shape\":\"rect\",\"coords\":\"214,14,237,32\"}]"} {"title":"Speed of light in a vacuum","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"281,15,294,33\"}]"} {"title":"Mass of a neutral hydrogen atom (1 proton + 1 electron","description":"Incorrect","type":"incorrect","color":"#ff6600","code":"[{\"shape\":\"rect\",\"coords\":\"148,16,169,32\"}]"} {"title":"Mass of a neutron","description":"Incorrect","type":"incorrect","color":"#0000ff","code":"[{\"shape\":\"rect\",\"coords\":\"76,15,97,31\"}]"}

Question

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{"title":"Binding energy of a nucleus","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"2,12,17,31\"}]"} {"title":"Number of neutrons in the nucleus","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"56,11,77,33\"}]"} {"title":"Number of protons in the nucleus","description":"Wrong","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"130,12,148,32\"}]"} {"title":"Mass of a neutral atom (including electrons) containing that nucleus","description":"Correct!","type":"correct","color":"#ff0000","code":"[{\"shape\":\"rect\",\"coords\":\"214,14,237,32\"}]"} {"title":"Speed of light in a vacuum","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"281,15,294,33\"}]"} {"title":"Mass of a neutral hydrogen atom (1 proton + 1 electron","description":"Incorrect","type":"incorrect","color":"#ff6600","code":"[{\"shape\":\"rect\",\"coords\":\"148,16,169,32\"}]"} {"title":"Mass of a neutron","description":"Incorrect","type":"incorrect","color":"#0000ff","code":"[{\"shape\":\"rect\",\"coords\":\"76,15,97,31\"}]"}

Question

bPc1Yg7xoR7yKjhmbmrt4oWiBz5cnkvqFSFY9UDw4ZQ=
{"title":"Binding energy of a nucleus","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"2,12,17,31\"}]"} {"title":"Number of neutrons in the nucleus","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"56,11,77,33\"}]"} {"title":"Number of protons in the nucleus","description":"Wrong","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"130,12,148,32\"}]"} {"title":"Mass of a neutral atom (including electrons) containing that nucleus","description":"Wrong","type":"incorrect","color":"#ff0000","code":"[{\"shape\":\"rect\",\"coords\":\"214,14,237,32\"}]"} {"title":"Speed of light in a vacuum","description":"Correct!","type":"correct","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"281,15,294,33\"}]"} {"title":"Mass of a neutral hydrogen atom (1 proton + 1 electron","description":"Incorrect","type":"incorrect","color":"#ff6600","code":"[{\"shape\":\"rect\",\"coords\":\"148,16,169,32\"}]"} {"title":"Mass of a neutron","description":"Incorrect","type":"incorrect","color":"#0000ff","code":"[{\"shape\":\"rect\",\"coords\":\"76,15,97,31\"}]"}

Question

gaEThimIcheyeBMCIB0tau47rMUY2nFIdPlu7Li92Z4oPv0rEdTkPJHPbbuDUSD9ZB3r+R1gJ2mKgKpi
{"title":"Binding energy of a nucleus","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"2,12,17,31\"}]"} {"title":"Number of neutrons in the nucleus","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"56,11,77,33\"}]"} {"title":"Number of protons in the nucleus","description":"Wrong","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"130,12,148,32\"}]"} {"title":"Mass of a neutral atom (including electrons) containing that nucleus","description":"Wrong","type":"incorrect","color":"#ff0000","code":"[{\"shape\":\"rect\",\"coords\":\"214,14,237,32\"}]"} {"title":"Speed of light in a vacuum","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"281,15,294,33\"}]"} {"title":"Mass of a neutral hydrogen atom (1 proton + 1 electron)","description":"Correct!","type":"correct","color":"#ff6600","code":"[{\"shape\":\"rect\",\"coords\":\"148,16,169,32\"}]"} {"title":"Mass of a neutron","description":"Incorrect","type":"incorrect","color":"#0000ff","code":"[{\"shape\":\"rect\",\"coords\":\"76,15,97,31\"}]"}

Question

e1qdm99yfR0B/CGF7E+kk6V4ifZtiTkK
{"title":"Binding energy of a nucleus","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"2,12,17,31\"}]"} {"title":"Number of neutrons in the nucleus","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"56,11,77,33\"}]"} {"title":"Number of protons in the nucleus","description":"Wrong","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"130,12,148,32\"}]"} {"title":"Mass of a neutral atom (including electrons) containing that nucleus","description":"Wrong","type":"incorrect","color":"#ff0000","code":"[{\"shape\":\"rect\",\"coords\":\"214,14,237,32\"}]"} {"title":"Speed of light in a vacuum","description":"Incorrect","type":"incorrect","color":"#333333","code":"[{\"shape\":\"rect\",\"coords\":\"281,15,294,33\"}]"} {"title":"Mass of a neutral hydrogen atom (1 proton + 1 electron)","description":"Wrong","type":"incorrect","color":"#ff6600","code":"[{\"shape\":\"rect\",\"coords\":\"148,16,169,32\"}]"} {"title":"Mass of a neutron","description":"Correct!","type":"correct","color":"#0000ff","code":"[{\"shape\":\"rect\",\"coords\":\"76,15,97,31\"}]"}

Review

To find the binding energy of \(\sideset{^4}{\mathrm{He}}{}\), we subtracted the mass of the nucleus from the mass of the two protons and two neutrons separately, and then multiplied by \(c^2\) to find the equivalent energy. In general, for a nucleus consisting of \(N\) neutrons and \(Z\)protons, \(E_{\mathrm{B}}\) is

\(E_{\mathrm{B}} =\left(N m_{\mathrm{n}} + Zm_{\mathrm{p}} - m_{\mathrm{nucleus}}\right)c^2\)

where \(m_{\mathrm{n}}\) is the mass of a neutron, \(m_{\mathrm{p}}\) is the mass of a proton, and \(m_{\mathrm{nucleus}}\) is the mass of the nucleus. In practice, it’s easier to measure the masses of neutral atoms (including their electrons) than the masses of isolated atomic nuclei. In terms of these masses, we can write the binding energy of a nucleus as