In 2014, the United States Postal Service charged $0.48 to mail a first class letter weighing upto 1oz. And $0.21 for each additional ounce. Based on these rates which function would determine the cost, in dollars, c(z), of meiling a first-class letter weighing z ounces where z is an integer greater than 1?

The postal rate for first-class mail is 44 cents for the first ounce or portion thereof and 17 cents for each additional ounce or portion thereof up to 3.5 ounces. The cost of a 3.5-ounce letter is 95cancel c . A formula for the cost in cents of first-class postage for a letter weighing N ounces (N le 3.5) is

Gina subscribes to a cell phone service that charges a monthly fee of $60.00 . The first 500 megabytes of data is free, and the cost is $0.15 for each additional megabyte of data used that month. Which of the following functions gives the cost, in dollars, for a month in which Gina uses x megabytes of data, where x gt 500 .

The equation of Schroedinger for the hydrogen atom in the time-independet, non-relativistic form is a partial differential equation involving the position coordinates (x, y and z). The potential energy term for the proton-electron system is spherically symmetric of the form -1//4pi in_(0) xx (e^(2)//r) . THus it is advantages to change over from the cartesian coordinates (x,y and z) to the spherical polar coordinates, (r, theta and phi ). In this form the equation become separable in the radial part involving r and the angular part involving theta and phi . The probability of locating the electron within a volume element d tau = 4pi r^(2)dr is then given |Psi|^(2)(4pir^(2)dr) , where Psi is a function of r, theta and phi . With proper conditions imposed on Psi , the treatment yields certain functions, Psi , known as atomic orbitals which are solutions of the equations. Each function Psi correspods to quantum number n, l and m, the principal, the azimuthal and the magnetic quantum number respectively, n has values 1, 2, 3,...., l has values 0, 1, 2, ....(n-1) for each value of n and m (n-1) for each value of n and m (m_(l)) has values =1, +(l+1),...1,0,-1,-2...-l i.e., (2l+1) values for each value of l. In addition a further quantum number called pin had to be introduced with values +-1//2 . Any set of four values for n, l , m and s characterizes a spin orbital. Pauli.s exclusion principle states that a given spin orbital can accomodate not more than electron. Further the values l = 0, l=1, l=2, l=3 are designated s,p,d and f orbitals respectively. It is a basic fact that any two electrons are indistinguishable. 3 electrons are to be accomodated in the spin orbitals included under the designated 2p, conforming to the Pauli principle. Calculate the number of ways in which this may be done.

The equation of Schroedinger for the hydrogen atom in the time-independet, non-relativistic form is a partial differential equation involving the position coordinates (x, y and z). The potential energy term for the proton-electron system is spherically symmetric of the form -1//4pi in_(0) xx (e^(2)//r) . THus it is advantages to change over from the cartesian coordinates (x,y and z) to the spherical polar coordinates, (r, theta and phi ). In this form the equation become separable in the radial part involving r and the angular part involving theta and phi . The probability of locating the electron within a volume element d tau = 4pi r^(2)dr is then given |Psi|^(2)(4pir^(2)dr) , where Psi is a function of r, theta and phi . With proper conditions imposed on Psi , the treatment yields certain functions, Psi , known as atomic orbitals which are solutions of the equations. Each function Psi correspods to quantum number n, l and m, the principal, the azimuthal and the magnetic quantum number respectively, n has values 1, 2, 3,...., l has values 0, 1, 2, ....(n-1) for each value of n and m (n-1) for each value of n and m (m_(l)) has values =1, +(l+1),...1,0,-1,-2...-l i.e., (2l+1) values for each value of l. In addition a further quantum number called pin had to be introduced with values +-1//2 . Any set of four values for n, l , m and s characterizes a spin orbital. Pauli.s exclusion principle states that a given spin orbital can accomodate not more than electron. Further the values l = 0, l=1, l=2, l=3 are designated s,p,d and f orbitals respectively. Which of the following diagrams corresponds to the 2s orbital ?

Answer the question based on the given sequence : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Counting from left if it is possible to make a meaningful word from the third and fifth letters from left, using each at least twice and third letter from right in sequence, only once, write the first letter of the word as your answer. If more than one such word can be formed write 'M' as your answer, and if no word can be formed write 'X' as your answer. 1) M 2) X 3) O 4) I 5) None of these

An orbital is designated by certain values of first three quantum numbers (n, l and m) and according to Pauli.s exclusion principle, no two electrons in a atom can have all the for quantum numbers equal. N, l and m denote size, shape and orientation of the orbital. The permissible values of n are 1,2,3.... prop while that of 1 are all possible integral values from 0 to n-n. Orbitals with same values of n and 1 but different values of m (where m can have any integral values from 1 to +1 including zero) are of equal energy and are called degenerate orbitals. However degeneracy is destroyed in homogeneous external magnetic field due to different extent of interaction between the applied field and internal electronic magnet of different orbitals differing in orientations. In octahedral magnetic field external magnetic field as oriented along axes while in tetrahedral field the applied field actas more in between the axes than that on the axes themselves. For 1=0, 1,2,3,...., the states (called sub-shells) are denoted by the symbol s,p,d,f.....respectively. After f, the subshells are denoted by letters alphabetically 1 determines orbital angular motion (L) of electron as L = sqrt(l(l+1))(h)/(2pi) ON the other hand, m determines Z-component of orbital angular momentum as L_(Z) = m((h)/(2pi)) Hund.s rule states that in degenerate orbitals electrons do not pair up unless and until each each orbitals has got an electron with parallesl spins Besides orbital motion,an electron also posses spin-motion. Spin may be clockwise and anticloskwise. Both these spin motions are called two spins states of electrons characterized by spin Q.N (s) : s = +(1)/(2) and = -(1)/(2) respectively The sum of spin Q.N. of all the electrons is called total spin(s) and 2s+1 is called spin multiplicity of the configuration as a whole. The spin angular momentum of an electron is written as L_(s) = sqrt(s(s+1))(h)/(2pi) The orbital angular momentum of electron (l=1) makes an angles of 45^(@) from Z-axis. The L_(z) of electron will be

The equation of Schroedinger for the hydrogen atom in the time-independet, non-relativistic form is a partial differential equation involving the position coordinates (x, y and z). The potential energy term for the proton-electron system is spherically symmetric of the form -1//4pi in_(0) xx (e^(2)//r) . THus it is advantages to change over from the cartesian coordinates (x,y and z) to the spherical polar coordinates, ( r, theta and phi ). In this form the equation become separable in the radial part involving r and the angular part involving theta and phi . The probability of locating the electron within a volume element d tau = 4pi r^(2)dr is then given |Psi|^(2)(4pir^(2)dr) , where Psi is a function of r, theta and phi . With proper conditions imposed on Psi , the treatment yields certain functions, Psi , known as atomic orbitals which are solutions of the equations. Each function Psi correspods to quantum number n, l and m, the principal, the azimuthal and the magnetic quantum number respectively, n has values 1, 2, 3,...., l has values 0, 1, 2, ....(n-1) for each value of n and m (n-1) for each value of n and m (m_(l)) has values =1, +(l+1),...1,0,-1,-2...-l i.e., (2l+1) values for each value of l. In addition a further quantum number called pin had to be introduced with values +-1//2 . Any set of four values for n, l , m and s characterizes a spin orbital. Pauli.s exclusion principle states that a given spin orbital can accomodate not more than electron. Further the values l = 0, l=1, l=2, l=3 are designated s,p,d and f orbitals respectively. How many spin orbitals are there corresponding to n = 3?

An orbital is designated by certain values of first three quantum numbers (n, l and m) and according to Pauli.s exclusion principle, no two electrons in a atom can have all the for quantum numbers equal. N, l and m denote size, shape and orientation of the orbital. The permissible values of n are 1,2,3.... prop while that of 1 are all possible integral values from 0 to n-n. Orbitals with same values of n and 1 but different values of m (where m can have any integral values from 1 to +1 including zero) are of equal energy and are called degenerate orbitals. However degeneracy is destroyed in homogeneous external magnetic field due to different extent of interaction between the applied field and internal electronic magnet of different orbitals differing in orientations. In octahedral magnetic field external magnetic field as oriented along axes while in tetrahedral field the applied field actas more in between the axes than that on the axes themselves. For 1=0, 1,2,3,...., the states (called sub-shells) are denoted by the symbol s,p,d,f.....respectively. After f, the subshells are denoted by letters alphabetically 1 determines orbital angular motion (L) of electron as L = sqrt(l(l+1))(h)/(2pi) ON the other hand, m determines Z-component of orbital angular momentum as L_(Z) = m((h)/(2pi)) Hund.s rule states that in degenerate orbitals electrons do not pair up unless and until each each orbitals has got an electron with parallesl spins Besides orbital motion,an electron also posses spin-motion. Spin may be clockwise and anticloskwise. Both these spin motions are called two spins states of electrons characterized by spin Q.N (s) : s = +(1)/(2) and = -(1)/(2) respectively The sum of spin Q.N. of all the electrons is called total spin(s) and 2s+1 is called spin multiplicity of the configuration as a whole. The spin angular momentum of an electron is written as L_(s) = sqrt(s(s+1))(h)/(2pi) According to Hund.s rule, the distribution of electron within the various orbitals of a given sub-shell is one which is associated with

Niels Bohr a Danish physicist received his PhD from the University of Copenhagen in 1911. He that spent a year with J.J. Thomson and Ernest Rutherford in England. In 1913, he returned to Copenhagen Where he remained for the rest of his life. In 1920 he was named Director of the Institute of theory! Physics After first World War Bohr worked energetically for peaceful uses of atomic energy recieved the first Atoms for Peace award in 1957 Bohr was awarded the Nobel Prize in Physics 1922 (a) The Angular momentum of an electron in a given stationary state can be expressed as m_e vr =h/(2pi) where n=1, 2,3 ...... Thus an electron can move only in those orbits for which its angular momentum is integral multiple of h/2 pi that is why only certain fixed orbits are alowed (b) The radii of the stationary states are expressed as r_n=n^2a_0 where a_0 =52.9 pm. Thus the radius the first stationary state, called the Bohr radius, is 52.9 pm. Normally the electron in the hydrogen atom is found in this orbit (that is n =1). As n increases the value of r will increase (c) The most important property associated with the electron E_n=-2.18xx10^(-18)(Z^2/n^2)J n=1,2,3 (d)it is also possible to calculate to calculate the velocities of electrons moving in these orbits by using v_n=2.18 10^6xxZ/n m/sec. Qualitatively the magnitude of velocity of electron increases with increase of positive charge on the nucleus and decreases with increases the value of n. (e)Bohr's theory can also be applied to th ions containing only one electron, similar to that present it hydrogen atom. For example , He^+ Li^(2+) , Be^(3+) and so on. given by the expression Ex=-218x n=1,2,3 (d) It is also possible to calculate the velocities of electrons moving in these orbits by using V 2.1810 cm/sec Qualitatively the magnitude of velocity of electron increases with increase of positive charge on the nucleus and decreases with increase the value of n (e) Bohr's theory can also be applied to the ions containing only one electron, similar to that presenti hydrogen atom For example, Help, Be and so on Choose the incorrect curve : if v=velocity of electron in Bohr's orbit r=Radius of electron in Bohr's orbit P.E.=Potential energy of electron in Bohr's orbit K.E.=Kinetic energy of the electron in Bohr's orbit.