Four electrons, each of mass me are in a...

Four electrons, each of mass `m_e` are in a one dimensional box of size L. Assume that the elections are non-interacting, obey the Pauli exclusion principle and are described by standing de Broglie waves confined within the box. Define `alpha =h^2//8m_eL^2` and `U_0` to be the ground state energy. Then

the energy of the highest occupied state is `16alpha`

`U_0=30 alpha`

the total energy of the first excited state is `U_0+9alpha`

The total energy of the second excited state is `U_0+8alpha`

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The position and energy of an electron is specified with the help of four quantum numbers namely, principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m_l) and spin quantum number (m_s) . The permissible values of these are : n = 1,2..... l = 0,1,.....(n-1) m_l = -l,......0,......+l m_s = +1/2 and -1/2 for each value of m_l . The angular momentum of electron is given as sqrt(l(l + 1)) cdot h/(2pi) While spin angular momentum is given as sqrt(s(s+1)) cdot (h/(2pi)) where s = 1/2 The electrons having the same value of n, l and m_l are said to belong to the same orbital. According to Pauli's exclusion principle, an orbital can have maximum of two electrons and these two must have opposite spin. For an electron having n = 3 and l = 0 , the orbital angular momentum is

Assume that the de Brogie wave associated with an electron can can from a standing wave between the atome arrange in a one dimensional array with nodes at each of the atomic sites it is found that one such standing wave if the distance d between the aloms of the arry is 2 M139 wave is again formad if d is increased to 2.5Å . A similar standing in the distance if d find the energy of the electrons velts and tghe least value of d for which the standing wave type described above can from .

One of the fundamental laws of physics is that matter is most stable with the lowest possible energy. Thus, the electron in a hydrogen atom usually moves in the n=1 orbit, the orbit in which it has the lowest energy. When the electon is in this lowest energy orbit, the atom is said to be in its ground electronic state. If the atom receives energy from an outside source, it is possible for the electron to move ot an orbit with a higher n value, in which case the atoms is in an excited state with a higher energy. The law of conservation of energy says that we cannot create or destroy energy. Thus, if a certain amount of external energy is required to excite an electron from one energy level to another, then that same amount of energy will be liberated when the electron returns to its initial state. Lyman series is observed when the electron returns to the lowest orbit while Balmer series is formed when the electron returns returns to second orbit. Similarly, Paschen, Brackett and Pfund series are formed when electrons returns to the third, fourth and fifth orbits from higher energy orbits respectively. When electrons return form n_(2) " to " n_(1) state, the number of lines in the spectrum will equal to ((n_(2)-n_(1))(n_(2)-n_(1)+1))/(2) If the electon comes back from energy level having energy E_(2) to energy level having energy E_(1) , then the difference may be expressed in terms of energy of photon as : E_(2)-E_(1)=DeltaE, deltaE implies (hc)/(lambda) Since, h and c are constant, deltaE corresponds to definite energy. Thus, each transition from one energy level to another will produce a radiatiob of definite wavelength. This is actually Wave number of a spectral line is given by the formula barv=R((1)/(n_(1)^(2))-(1)/(n_(2)^(2))) . where R is a Rydberg's constant (R=1.1xx10^(7) m^(-1)) An electron in H-atom in M-shell on de-excitation to ground state gives maximum ........... spectrum lines.

One of the fundamental laws of physics is that matter is most stable with the lowest possible energy. Thus, the electron in a hydrogen atom usually moves in the n=1 orbit, the orbit in which it has the lowest energy. When the electon is in this lowest energy orbit, the atom is said to be in its ground electronic state. If the atom receives energy from an outside source, it is possible for the electron to move ot an orbit with a higher n value, in which case the atoms is in an excited state with a higher energy. The law of conservation of energy says that we cannot create or destroy energy. Thus, if a certain amount of external energy is required to excite an electron from one energy level to another, then that same amount of energy will be liberated when the electron returns to its initial state. Lyman series is observed when the electron returns to the lowest orbit while Balmer series is formed when the electron returns returns to second orbit. Similarly, Paschen, Brackett and Pfund series are formed when electrons returns to the third, fourth and fifth orbits from higher energy orbits respectively. When electrons return form n_(2) " to " n_(1) state, the number of lines in the spectrum will equal to ((n_(2)-n_(1))(n_(2)-n_(1)+1))/(2) If the electon comes back from energy level having energy E_(2) to energy level having energy E_(1) , then the difference may be expressed in terms of energy of photon as : E_(2)-E_(1)=DeltaE, deltaE implies (hc)/(lambda) Since, h and c are constant, deltaE corresponds to definite energy. Thus, each transition from one energy level to another will produce a radiatiob of definite wavelength. This is actually Wave number of a spectral line is given by the formula barv=R((1)/(n_(1)^(2))-(1)/(n_(2)^(2))) . where R is a Rydberg's constant (R=1.1xx10^(7) m^(-1)) The emission spectra is observed by the consequence of transition of electrons from higher energy state to ground state of He^(+) ion. Six different photons are observed during the emission spectra, then what will be the minimum wavelength during the transition?

One of the fundamental laws of physics is that matter is most stable with the lowest possible energy. Thus, the electron in a hydrogen atom usually moves in the n=1 orbit, the orbit in which it has the lowest energy. When the electon is in this lowest energy orbit, the atom is said to be in its ground electronic state. If the atom receives energy from an outside source, it is possible for the electron to move ot an orbit with a higher n value, in which case the atoms is in an excited state with a higher energy. The law of conservation of energy says that we cannot create or destroy energy. Thus, if a certain amount of external energy is required to excite an electron from one energy level to another, then that same amount of energy will be liberated when the electron returns to its initial state. Lyman series is observed when the electron returns to the lowest orbit while Balmer series is formed when the electron returns returns to second orbit. Similarly, Paschen, Brackett and Pfund series are formed when electrons returns to the third, fourth and fifth orbits from higher energy orbits respectively. When electrons return form n_(2) " to " n_(1) state, the number of lines in the spectrum will equal to ((n_(2)-n_(1))(n_(2)-n_(1)+1))/(2) If the electon comes back from energy level having energy E_(2) to energy level having energy E_(1) , then the difference may be expressed in terms of energy of photon as : E_(2)-E_(1)=DeltaE, deltaE implies (hc)/(lambda) Since, h and c are constant, deltaE corresponds to definite energy. Thus, each transition from one energy level to another will produce a radiatiob of definite wavelength. This is actually Wave number of a spectral line is given by the formula barv=R((1)/(n_(1)^(2))-(1)/(n_(2)^(2))) . where R is a Rydberg's constant (R=1.1xx10^(7) m^(-1)) If the wavelength of series limit of Lyman series for He^(+) ion is x Å, then what will be the wavelength of series limit of Balmer series for Li^(2+) ion?

One of the fundamental laws of physics is that matter is most stable with the lowest possible energy. Thus, the electron in a hydrogen atom usually moves in the n=1 orbit, the orbit in which it has the lowest energy. When the electon is in this lowest energy orbit, the atom is said to be in its ground electronic state. If the atom receives energy from an outside source, it is possible for the electron to move ot an orbit with a higher n value, in which case the atoms is in an excited state with a higher energy. The law of conservation of energy says that we cannot create or destroy energy. Thus, if a certain amount of external energy is required to excite an electron from one energy level to another, then that same amount of energy will be liberated when the electron returns to its initial state. Lyman series is observed when the electron returns to the lowest orbit while Balmer series is formed when the electron returns returns to second orbit. Similarly, Paschen, Brackett and Pfund series are formed when electrons returns to the third, fourth and fifth orbits from higher energy orbits respectively. When electrons return form n_(2) " to " n_(1) state, the number of lines in the spectrum will equal to ((n_(2)-n_(1))(n_(2)-n_(1)+1))/(2) If the electon comes back from energy level having energy E_(2) to energy level having energy E_(1) , then the difference may be expressed in terms of energy of photon as : E_(2)-E_(1)=DeltaE, deltaE implies (hc)/(lambda) Since, h and c are constant, deltaE corresponds to definite energy. Thus, each transition from one energy level to another will produce a radiatiob of definite wavelength. This is actually Wave number of a spectral line is given by the formula barv=R((1)/(n_(1)^(2))-(1)/(n_(2)^(2))) . where R is a Rydberg's constant (R=1.1xx10^(7) m^(-1)) What transition in the hydrogen spectrum would have the same wavelength as Balmer transitio, n=4 " to "n=2 in the He^(+) spectrum?

The position and energy of an electron is specified with the help of four quantum numbers namely, principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m_l) and spin quantum number (m_s) . The permissible values of these are : n = 1,2..... l = 0,1,.....(n-1) m_l = -l,......0,......+l m_s = +1/2 and -1/2 for each value of m_l . The angular momentum of electron is given as sqrt(l(l + 1)) cdot h/(2pi) While spin angular momentum is given as sqrt(s(s+1)) cdot (h/(2pi)) where s = 1/2 The electrons having the same value of n, l and m_l are said to belong to the same orbital. According to Pauli's exclusion principle, an orbital can have maximum of two electrons and these two must have opposite spin. The maximum number of electrons having n + l = 5 in an atom is

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