Tuesday, 29 May 2018

How Were The Elements Created?

    By Akash Peshin
One of the most beautiful things I’ve ever read in my life is that we are literally the remnants of stars. “The nitrogen in our DNA, the calcium in our teeth, the iron in our blood, the carbon in our apple pies were made in the interiors of collapsing stars”, wrote Carl Sagan, concluding, “We are made of star stuff.”
The Orion Nebula, one of our nearest star nurseries. (Photo Credit: peresanz / Fotolia)
The elements that comprise life are the scattered ashes of stars after they suffer horrific, explosive deaths. So, in a way, they died so you could be born. However, not all elements in the periodic table were created in the core of a star. A few were created outside it, by nature, and the rest, by us. Let’s first understand how some were created inside a core, which requires us to examine the life of a star.

Natural Elements

The lightest elements hydrogen and helium were created when the dust settled after the Big Bang. A nascent star comprises mostly this hydrogen gas collapsing in on itself. This compression heats the gas and forces its atoms to collide violently with each other. The collisions further heat the gas and eventually the hydrogen atoms don’t collide and ricochet, but instead fuse to form helium atoms!
The mass of a helium atom is less than the combined mass of two hydrogen atoms. The remaining mass is released as energy whose magnitude is given by Einstein’s E = mc². While the magnitude might be small for a single fusion reaction, the cumulative total is tremendous. This process is called nuclear fusion. The same principle that makes stars shine is replicated inside devastating hydrogen bombs, albeit in a controlled manner.
Hydrogen atoms fusion reaction
Eventually, the star runs out of fuel. All the hydrogen is exhausted. However, the compression and sweltering heat now force helium atoms to fuse and form beryllium! Eventually, the beryllium atoms are forced to fuse and form carbon and then oxygen and so on until iron is synthesized in the core. At this point, the star is exorbitantly massive – two or three times the mass of the Sun. However, it can no longer counteract gravity’s compression because iron refuses to undergo further fusion. With no fuel and no heat to expand, the star begins to cool and contract.
In the final stages of its life, the star can get millions of tons per cubic inch dense as all the heavier elements are clustered in a sphere with a radius of merely 10 miles. However, further contraction collapses the star to a point of infinite density! But before collapsing into a black hole, it cataclysmically explodes with the energy of an octillion (10²⁷) atomic bombs!
Most distant Gamma ray burst
Supernovae release a tremendous amount of energy in this short time making them the most powerful events in the Universe. (Photo Credit : ESO/A. Roquette / Wikipedia Commons)
The explosive death of a star is called a supernova and it is the most colossal explosion one can witness in space. All the elements inside the core are violently dispersed into the surroundings. What’s more, the heat released is so intense that the elements undergo nuclear reactions that weren’t previously possible inside the core. The elements are bombarded with haphazard, scampering neutrons to create even more elements. Iron turns into gold, which turns into lead and so on until uranium is formed, the heaviest naturally synthesized element. Thus, destruction breeds creation.

Man-Made Elements

The entire Solar System was created from a similar rubble dispersed by a supernova. Can you imagine the staggering amount of dust and debris that accrued to form not just the Sun, but eight planets and a dwarf that devotedly revolve around it?

However, like I said, not all elements are created in the core or outside it. Uranium is the 92nd element, so how did the other 27 spring into existence? While plutonium and neptunium can be synthesized in a supernova, their traces might not be substantial. These elements can be synthesized naturally. Perhaps the stars create elements much heavier than we ever can, but these elements cannot survive more than a few microseconds — they immediately decay into lighter elements.
Americium decay
Man then took the laws of nature into his own hands when the technology sufficed. Elements heavier than uranium were created by simply bombarding uranium with high-speed neutrons in cyclotrons. A chain reaction ensues that might involve as many as 17 neutrons. This process, however, can also occur in ‘natural’ nuclear reactors or heavy deposits of uranium beneath the Earth. The meager quantity of plutonium and neptunium on Earth are found in uranium deposits where they formed a billion years ago when the uranium was pelted with free neutrons.
However, fermium (100) is the last element that can be forged by nuclear bombardment. The super-heavy elements could only be created after the development of particle accelerators more superiorly advanced than cyclotrons. The new elements weren’t created by just bombarding existent atoms with neutrons, but with entire atoms. Consider mendelevium (101), which was synthesized by fusing helium (2) and einsteinium (99), or nobelium (102), a coalition of neon (10) and uranium (92). Or, the final, 118th element, oganesson, which was created by fusing californium (98) and calcium (20).
Ironman 2 particle accelerator scene
Tony Stark synthesized Vibranium, the strongest element in the Marvel Universe, with a particle accelerator he built in his own house. Only if it were that simple. (Photo Credit: Iron Man 2 / Marvel Studios)
The question that is yet to be answered is whether there exists a limit to synthesizing heavier and heavier elements. People usually ask how protons can reside so close in a nucleus when the electromagnetic repulsive force should throw them apart. The force that binds them, however, is stronger than the repulsive force. In fact, it is the strongest of the four fundamental forces that govern the ways of the Universe. It is called — with the utmost lack of creativity — the strong force.
But even the strong force has its limits. There is certainly a configuration of protons in which the cumulative repulsive force between them becomes potent enough to overthrow the strong force binding them. Surely, the key to creating a new element is to avoid this configuration. This is our limit beyond which the laws of physics refuse to cooperate. However, it seems like we aren’t too far away. The periodic table seems to be nearly finished. We’re only a handful of revelations away from completing the puzzle.

source: scienceabc

Saturday, 26 May 2018

A list of Formulae and equations widely used

Mechanics
velocity
 = Δs
Δt
v = ds
dt
acceleration
 = Δv
Δt
a = dv
dt
equations of motion
v = v0 + at
s = s0 + v0t + ½at2
v2 = v02 + 2a(s − s0)
 = ½(v + v0)
newton's 2nd law
F = ma
F = dp
dt
weight
W = mg
dry friction
fs ≤ μsN
fk = μkN
centripetal accel.
ac = v2
r
ac = − ω2r
momentum
p = mv
impulse
J = Δt
J = 
F dt
impulse-momentum
Δt = mΔv

F dt = Δp
work
W = Δs cos θ
W = 
F · ds
work-energy
Δs cos θ = ΔE

F · ds = ΔE
kinetic energy
K = ½mv2
K = p2
2m
general p.e.
ΔU = − 
F · ds
F = − ∇U
gravitational p.e.
ΔUg = mgΔh
efficiency
η = Wout
Ein
power
 = ΔW
Δt
P = dW
dt
power-velocity
P = Fv cos θ
P = F · v
angular velocity
ω̅ = Δθ
Δt
ω = dθ
dt
v = ω × r
angular acceleration
α̅ = Δω
Δt
α = dω
dt
a = α × r − ω2 r
equations of rotation
ω = ω0 + αt
θ = θ0 + ω0t + ½αt2
ω2 = ω02 + 2α(θ − θ0)
ω̅ = ½(ω + ω0)
torque
τ = rF sin θ
τ = r × F
2nd law for rotation
τ = Iα
τ = dL
dt
moment of inertia
I = ∑mr2
I = 
 r2 dm
rotational work
W = τ̅Δθ
W = 
 τ · dθ
rotational power
P = τω cos θ
P = τ · ω
rotational k.e.
K = ½Iω2
angular momentum
L = mrv sin θ
L = r × p
L = Iω
universal gravitation
Fg = − Gm1m2 
r2
gravitational field
g = − Gm 
r2
gravitational p.e.
Ug = − Gm1m2
r
gravitational potential
Vg = − Gm
r
orbital speed
v = √Gm
r
escape speed
v = √2Gm
r
hooke's law
F = − kΔx
elastic p.e.
Us = ½kΔx2
s.h.o.
T = 2π √m
k
simple pendulum
T = 2π √
g
frequency
f = 1
T
angular frequency
ω = 2πf
density
ρ = m
V
pressure
P = F
A
pressure in a fluid
P = P0 + ρgh
buoyancy
B = ρgVdisplaced
mass flow rate
qm = m
t
volume flow rate
qV = V
t
mass continuity
ρ1A1v1 = ρ2A2v2
volume continuity
A1v1 = A2v2
bernoulli's equation
P1 + ρgy1 + ½ρv12 = P2 + ρgy2 + ½ρv22
dynamic viscosity
 = η Δvx
AΔz
F = η dvx
Adz
kinematic viscosity
ν = η
ρ
drag
R = ½ρCAv2
mach number
Ma = v
c
reynolds number
Re = ρvD
η
froude number
Fr = v
g
young's modulus
F = E Δℓ
A0
shear modulus
F = G Δx
Ay
bulk modulus
F = K ΔV
AV0
surface tension
γ = F

Thermal Physics

solid expansion
Δℓ = αℓ0ΔT
ΔA = 2αA0ΔT
ΔV = 3αV0ΔT
liquid expansion
ΔV = βV0ΔT
sensible heat
Q = mcΔT
latent heat
Q = mL
ideal gas law
PV = nRT
molecular constants
nR =Nk
maxwell-boltzmann
− mv2
p(v) = 4v2
m3/2
e2kT
√π2kT
molecular k.e.
K⟩ = 32kT
molecular speeds
vp = √2kT
m
v⟩ = √8kT
πm
vrms = √3kT
m
heat flow rate
Φ̅ = ΔQ
Δt
Φ = dQ
dt
thermal conduction
Φ = kAΔT
stefan-boltzmann law
Φ = εσA(T4 − T04)
wien displacement law
λmax = b
T
internal energy
ΔU = 32nRΔT
ΔU = 32NkΔT
thermodynamic work
W = −
P dV
1st law of thermo.
ΔU = Q + W
entropy
ΔS = ΔQ
T
S = k log w
efficiency
ηreal = 1 − QC
QH
ηideal = 1 − TC
TH
c.o.p.
COPreal = QC
QH − QC
COPideal = TC
TH − TC

Waves & Optics

periodic waves
v = fλ
frequency
f = 1
T
beat frequency
fbeat = fhigh − flow
intensity
I = P
A
intensity level
LI = 10 log
I
I0
pressure level
LP = 20 log
P
P0
interference fringes
nλ = d sin θ
nλ ≈ x
dL
index of refraction
n = c
v
snell's law
n1 sin θ1 = n2 sin θ2
critical angle
sin θc = n2
n1
image location
1 = 1 + 1
fdodi
image size
M = hi = di
hodo
spherical mirrors
f ≈ r
2

Electricity & Magnetism

coulomb's law
F = k q1q2
r2
F = 1 q1q2 
4πε0r2
electric field, def.
E = FE
q
electric potential, def.
ΔV = ΔUE
q
field & potential
 = − V
d
E = − ∇V
electric field
E = k ∑q 
r2
E = k 
dq 
r2
electric potential
V = k ∑q
r
V = k 
dq
r
capacitance
C = Q
V
plate capacitor
C = κε0A
d
cylindrical capacitor
C = 2πκε0
ln(b/a)
spherical capacitor
C = 4πκε0
(1/a) − (1/b)
capacitive p.e.
U = 1 CV2 = 1 Q2 = 1 QV
22C2
electric current
 = Δq
Δt
I = dq
dt
ohm's law
V = IR
E = ρJ
J = σE
resitivity-conductivity
ρ = 1
σ
electric resistance
R = ρℓ
A
electric power
P = VI = I2R = V2
R
resistors in series
Rs = ∑Ri
resistors in parallel
1 = ∑1
RpRi
capacitors in series
1 = ∑1
CsCi
capacitors in parallel
Cp = ∑Ci
magnetic force, charge 
FB = qvB sin θ
FB = qv × B
magnetic force, current
FB = IB sin θ
dFB = I d × B
biot-savart law
B = μ0I
ds × 
r2
solenoid
B = µ0nI
straight wire
B = μ0I
r
parallel wires
FB = μ0 I1I2
r
electric flux
ΦE = EA cos θ
ΦE = 
E · dA
magnetic flux
ΦB = BA cos θ
ΦB = 
B · dA
motional emf
ℰ = Bv
induced emf
ℰ̅ = − ΔΦB
Δt
ℰ = − dΦB
dt

gauss's law
E · dA = Q
ε0
∇ · E = ρ
ε0
no one's law
B · dA = 0 
 
∇ · B = 0
 
faraday's law
E · ds = − ∂ΦB
t
∇ × E = − B
t
ampere's law
B · ds = μ0ε0 ∂ΦE + μ0I
t
∇ × B = μ0ε0 E + μ0 J
t

Modern Physics

lorentz factor
γ = 1
√(1 − v2/c2)
time dilation
t' = t
√(1 − v2/c2)
t' = γt
length contraction
ℓ' = ℓ √(1 − v2/c2)
ℓ' = 
γ
relative velocity
u' = u + v
1 + uv/c2
relativistic energy
E = mc2
√(1 − v2/c2)
E = γmc2
relativistic momentum
p = mv
√(1 − v2/c2)
p = γmv
energy-momentum
E2 = p2c2 + m2c4
mass-energy
E = mc2
relativistic k.e.
K = 
1 − 1
mc2
√(1 − v2/c2)
K = (γ − 1)mc2
relativistic doppler effect
λ = f0 = √
1 + v/c
λ0f1 − v/c
photon energy
E = hf
E = pc
photon momentum
p = h
λ
p = E
c
photoelectric effect
Kmax = E − ϕ
Kmax = h(f − f0)
schroedinger's equation
iℏ  Ψ(r,t) = − 2 ∇2Ψ(r,t) + V(r)Ψ(r,t)
∂t2m
Eψ(r) = − 2 ∇2ψ(r) + V(r)ψ(r)
2m
uncertainty principle
ΔpxΔx ≥ ℏ 
2
ΔEΔt ≥ ℏ 
2
rydberg equation
1 = −R 
1 − 1
λn2n02
half life
N = N02t/T½
absorbed dose
D = E
m
effective dose
H = QD
Source: physics.info
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